BuboFlash - helps with learning

Edited, memorised or added to reading queue

Do you want BuboFlash to help you learning these things? Click here to log in or create user.

Flashcard 150890360

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

Consider the multiplicative model X_t = m_t × s_t × W_t .Let Y_t denote the time series of logarithms: Y_t =log X_t .Then

Y_t =log X_t
Y_t= log(m_t × s_t × W_t)
Y_t= [...] .

Answer

log m_t +log s_t +log W_t

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Consider the multiplicative model X t = m t × s t × W t .Let Y t denote the time series of logarithms: Y t =log X t .Then Y t =log X t Y t = log(m t × s t × W t ) Y t = log m t +log s t +log W t .

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890373

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

if a [...] model is appropriate for the time series X_t , then an additive model is appropriate for the time series of logarithms, Y_t =log X_t .

Answer

multiplicative

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
if a multiplicative model is appropriate for the time series X t , then an additive model is appropriate for the time series of logarithms, Y t =log X t .

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890379

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

if a multiplicative model is appropriate for the time series X_t , then [...] model is appropriate for the time series of logarithms, Y_t =log X_t .

Answer

an additive

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
if a multiplicative model is appropriate for the time series X t , then an additive model is appropriate for the time series of logarithms, Y t =log X t .

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890385

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

if a multiplicative model is appropriate for the time series X_t , then an additive model is appropriate for the time series of logarithms, Y_t = [...] .

Answer

log X_t

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
if a multiplicative model is appropriate for the time series X t , then an additive model is appropriate for the time series of logarithms, Y t =log X t .

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890398

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

by [...], a time series for which a multiplicative model is appropriate can be transformed into a time series for which an additive model is appropriate.

Answer

taking logarithms

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
by taking logarithms, a time series for which a multiplicative model is appropriate can be transformed into a time series for which an additive model is appropriate.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890411

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

Transformations of time series that are commonly used include the power transformations:
Y_t = [...] , where a = ... 1/4, 1/3, 1/2, 2, 3, 4, ....

Answer

X_t^a

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Transformations of time series that are commonly used include the power transformations: Y t = X t a , where a = ... 1/4, 1/3, 2, 3, 4, ....

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890417

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

Transformations of time series that are commonly used include the power transformations:
Y_t = X_t^a , where a = [...].

Answer

... 1/4, 1/3, 1/2, 2, 3, 4, ...

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Transformations of time series that are commonly used include the power transformations: Y t = X t a , where a = ... 1/4, 1/3, 2, 3, 4, ....

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890430

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

A [...] of order (or span) 11 can be written as Y_t = \(\large \frac{1}{11}\)(X_t−5 + ···+ X_t + ···+ X_t+5 )

Answer

simple moving average (or just a moving average)

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A simple moving average (or just a moving average) of order (or span) 11 can be written as Y t = 111(X t−5 + ···+ X t + ···+ X t+5 )

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890436

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

A simple moving average (or just a moving average) of [...] 11 can be written as Y_t = \(\large \frac{1}{11}\)(X_t−5 + ···+ X_t + ···+ X_t+5 )

Answer

order (or span)

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A simple moving average (or just a moving average) of order (or span) 11 can be written as Y t = 111(X t−5 + ···+ X t + ···+ X t+5 )

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890442

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

A simple moving average (or just a moving average) of order (or span) 11 can be written as Y_t = [...]

Answer

Y_t= \(\large \frac{1}{11}\)(X_t−5 + ···+ X_t + ···+ X_t+5 )

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A simple moving average (or just a moving average) of order (or span) 11 can be written as Y t = 111(X t−5 + ···+ X t + ···+ X t+5 )

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890455

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

For the purpose of smoothing time series, only moving averages for which the order is an odd number will be used. These are said to be [...] on the middle value.

Answer

centred

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
For the purpose of smoothing time series, only moving averages for which the order is an odd number will be used. These are said to be centred on the middle value.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890471

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

With a suitable degree of smoothing — that is, with a suitable choice of the order of the moving average — the moving average provides [...] of the trend component m_t ; this is denoted \(\hat{m_t}\)

Answer

an estimate

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
With a suitable degree of smoothing — that is, with a suitable choice of the order of the moving average — the moving average provides an estimate of the trend component m t ; this is denoted mt^

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890559

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

A [...] moving average of order 2q + 1 has the form
MA(t)= a_−q X_t−q + ···+ a₋₁ X_t−1 + a₀ X_t + a₁ X_t+1 + ···+ a_q X_t+q ,
where the weights a_j , j = −q, −q +1,... ,q, add up to 1.

Answer

weighted

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890565

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

A weighted moving average of order [...] has the form
MA(t)= a_−q X_t−q + ···+ a₋₁ X_t−1 + a₀ X_t + a₁ X_t+1 + ···+ a_q X_t+q ,
where the weights a_j , j = −q, −q +1,... ,q, add up to 1.

Answer

2q + 1

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,q, add up to 1.</

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890571

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

A weighted moving average of order 2q + 1 has the form
MA(t)= _[...] ,
where the weights a_j , j = −q, −q +1,... ,q, add up to 1.

Answer

a_−q X_t−q + ···+ a₋₁ X_t−1 + a₀ X_t + a₁ X_t+1 + ···+ a_q X_t+q

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,q, add up to 1.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890577

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

A weighted moving average of order 2q + 1 has the form
MA(t)= a_−q X_t−q + ···+ a₋₁ X_t−1 + a₀ X_t + a₁ X_t+1 + ···+ a_q X_t+q ,
where the weights a_j , j = −q, −q +1,... ,q, add up to [...].

Answer

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
l>A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,q, add up to 1.<html>

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890590

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

The weighted moving averages are denoted [...] rather than MA(t) when their particular use in smoothing out seasonal variation.

Answer

SA(t)

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The weighted moving averages are denoted SA(t) rather than MA(t) when their particular use in smoothing out seasonal variation.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890596

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

The weighted moving averages are denoted SA(t) rather than MA(t) when their particular use in smoothing out [...].

Answer

seasonal variation

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The weighted moving averages are denoted SA(t) rather than MA(t) when their particular use in smoothing out seasonal variation.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890609

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

The ﬁrst step is to ﬁnd an initial estimate of the trend component m_t that is not unduly inﬂuenced by the seasonal component s_t. A reasonable starting point would be to use a simple moving average with order equal to [...]. Such a moving average would smooth out the seasonal variation, as the annual highs and lows would cancel out.

Answer

the period T of the seasonal cycle

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
ead>The ﬁrst step is to ﬁnd an initial estimate of the trend component m t that is not unduly inﬂuenced by the seasonal component s t . A reasonable starting point would be to use a simple moving average with order equal to the period T of the seasonal cycle. Such a moving average would smooth out the seasonal variation, as the annual highs and lows would cancel out.<html>

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890615

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

Suppose that the data are quarterly, so that T = 4; can we use simple moving average with period T = 4 to smoothen out seasonal variations?

Answer

No, the period is an even number.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 150890624

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

Suppose that the data are quarterly, so that T = 4; to smoothen out seasonal variations we cannot use simple moving average with period T = 4 (because number is even), and if we use T = 5, one season (e.g. winter and next winter) would be counted twice. How to recover from this?

Answer

Use T = 5 weighted average and weight down the season counted twice with 0.5 (relative to other periods' weights).

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 150890643

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

The simple moving average is a weighted moving average in which the weights a_j are all equal to [...]

Answer

N⁻¹

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The simple moving average is a weighted moving average in which the weights a j are all equal to (2q +1) −1

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890954

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

One way to predict tomorrow’s average temperature is to assume it will be the same as [...].

Answer

today’s

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
One way to predict tomorrow’s average temperature is to assume it will be the same as today’s.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150890996

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

If a time series X_t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula
\(\hat{x}_{n+1}\) = [...]
where:

x_n is the observed value at time n,
\(\hat{x}_n\)and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X_n and X_n+1,
and α is a smoothing parameter, 0 ≤ α ≤ 1.

The method requires an initial value \(\hat{x}_1\), which is often chosen to be x₁ : \(\hat{x}_1\) = x₁.

Answer

\(\hat{x}_{n+1}\) = αx_n + (1 − α)\(\hat{x}_n\)

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150891005

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

x_n is the observed value at time n,
\(\hat{x}_n\)and \(\hat{x}_{n+1}\)are [...]
and α is a smoothing parameter, 0 ≤ α ≤ 1.

The method requires an initial value \(\hat{x}_1\), which is often chosen to be x₁ : \(\hat{x}_1\) = x₁.

Answer

the 1-step ahead forecasts of X_n and X_n+1,

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
t level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \hat{x}_nand \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n+1 , and α is a smoothing parameter, 0 ≤ α ≤ 1. The method requires an initial value \hat{x}_1, which is often chosen to be x 1 : \hat{x}_1 = x 1 .<body><html>

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150891011

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

x_n is the observed value at time n,
\(\hat{x}_n\)and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X_n and X_n+1,
and α is [...].

The method requires an initial value \(\hat{x}_1\), which is often chosen to be x₁ : \(\hat{x}_1\) = x₁.

Answer

a smoothing parameter, 0 ≤ α ≤ 1

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
e obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \hat{x}_nand \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n+1 , and α is a smoothing parameter, 0 ≤ α ≤ 1. The method requires an initial value \hat{x}_1, which is often chosen to be x 1 : \hat{x}_1 = x 1 .<body><html>

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150891017

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

If a time series X_t is described by an [...] model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula
\(\hat{x}_{n+1}\) = αx_n + (1 − α)\(\hat{x}_n\)
where:

x_n is the observed value at time n,
\(\hat{x}_n\) and \(\hat{x}_{n+1}\) are the 1-step ahead forecasts of X_n and X_n+1,
and α is a smoothing parameter, 0 ≤ α ≤ 1.

The method requires an initial value \(\hat{x}_1\), which is often chosen to be x₁ : \(\hat{x}_1\) = x₁.

Answer

additive

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150891023

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

If a time series X_t is described by an additive model with [...] level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula
\(\hat{x}_{n+1}\) = αx_n + (1 − α)\(\hat{x}_n\)
where:

x_n is the observed value at time n,
\(\hat{x}_n\)and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X_n and X_n+1,
and α is a smoothing parameter, 0 ≤ α ≤ 1.

The method requires an initial value \(\hat{x}_1\), which is often chosen to be x₁ : \(\hat{x}_1\) = x₁.

Answer

constant

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150891029

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

If a time series X_t is described by an additive model with constant level and [...] seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula
\(\hat{x}_{n+1}\) = αx_n + (1 − α)\(\hat{x}_n\)
where:

x_n is the observed value at time n,
\(\hat{x}_n\)and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X_n and X_n+1,
and α is a smoothing parameter, 0 ≤ α ≤ 1.

The method requires an initial value \(\hat{x}_1\), which is often chosen to be x₁ : \(\hat{x}_1\) = x₁.

Answer

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150891035

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

If a time series X_t is described by an additive model with constant level and no seasonality, [...]-step ahead forecasts may be obtained by simple exponential smoothing using the formula
\(\hat{x}_{n+1}\) = αx_n + (1 − α)\(\hat{x}_n\)
where:

x_n is the observed value at time n,
\(\hat{x}_n\)and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X_n and X_n+1,
and α is a smoothing parameter, 0 ≤ α ≤ 1.

The method requires an initial value \(\hat{x}_1\), which is often chosen to be x₁ : \(\hat{x}_1\) = x₁.

Answer

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150891041

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

If a time series X_t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple [...] using the formula
\(\hat{x}_{n+1}\) = αx_n + (1 − α)\(\hat{x}_n\)
where:

x_n is the observed value at time n,
\(\hat{x}_n\)and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X_n and X_n+1,
and α is a smoothing parameter, 0 ≤ α ≤ 1.

The method requires an initial value \(\hat{x}_1\), which is often chosen to be x₁ : \(\hat{x}_1\) = x₁.

Answer

exponential smoothing

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
If a time series X t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \hat{x}_nand \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150891047

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

x_n is the observed value at time n,
\(\hat{x}_n\)and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X_n and X_n+1,
and α is a smoothing parameter, 0 ≤ α ≤ 1.

The method requires an initial value \(\hat{x}_1\), which is often chosen to be [...].

Answer

\(\hat{x}_1\) = x₁

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 150891359

Tags

#m249 #mathematics #open-university #statistics #time-series

Question

what does the expanded m-times (i.e. non recursive) simple exponential smoothing formula looks like?
fully recursive is:
\(\hat{x}_{n+1}\)= αx_n + (1 − α)\(\hat{x}_n\)

Answer

expanded m-times is
\(\large \hat{x}_{n+1} = \sum_{i=0}^m\alpha(1-\alpha)^ix_{n-i}+(1-\alpha)^{m+1}\hat{x}_{n-m}\)

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
If a time series X t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula \(\hat{x}_{n+1}\)= αx n + (1 − α)\(\hat{x}_n\) where: x n is the observed value at time n, \(\hat{x}_n\)and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X n and X n+1 , and α is a smoothing parameter, 0 ≤ α ≤ 1.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1332009897228

Tags

#quantitative-methods-basic-concepts #statistics

Question

A [...] is defined as a numerical quantity (such as the mean) calculated in a sample.

Answer

statistic

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A statistic is defined as a numerical quantity (such as the mean) calculated in a sample.

Original toplevel document

Subject 1. The Nature of Statistics
Estimates of these parameters taken from a sample are called statistics. Much of the field of statistics is devoted to drawing inferences from a sample concerning the value of a population parameter. A statistic is defined as a numerical quantity (such as the mean) calculated in a sample. It has two different meanings. Most commonly, statistics refers to numerical data such as a company's earnings per share or average returns over the past five years. Statistics can also refer to the process of collecting, organizing, presenting, analyzing, and interpreting numerical data for the purpose of making decisions. Note that we will always know the exact composition of our sample, and by definition, we will always know the values within our sample. Ascertaining this information is the purpose of samples. Sample statistics will always be known, and can be used to estimate unknown population parameters. Hint: One way to easily remember these terms is to recall that "population" and "parameter" both start with a "p," and "sample" and "statisti

Flashcard 1332011470092

Tags

#quantitative-methods-basic-concepts #statistics

Question

A statistic is defined as a numerical quantity (such as the mean) calculated in a [...]

Answer

sample.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A statistic is defined as a numerical quantity (such as the mean) calculated in a sample.

Original toplevel document

Flashcard 1332018023692

Tags

#quantitative-methods-basic-concepts #statistics

Question

the order of the different scales is [...]

Answer

NOIR (the French word for black)

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
the order of the different scales is NOIR (the French word for black)

Original toplevel document

Subject 2. Measurement Scales
ey. Both examples can be measured on a zero scale, where zero represents no return, or in the case of money, no money. Note that as you move down through this list, the measurement scales get stronger. Hint: Remember the order of the different scales by remembering NOIR (the French word for black); the first letter of each word in the scale is indicated by the letters in the word NOIR. Before we move on, here's a quick exercise to make sure that you understand the different measurement scales. In each case, identify whether you think the data is nominal, ordinal, inter

Flashcard 1332022742284

Tags

#quantitative-methods-basic-concepts #statistics

Question

A [...] is a numerical quantity measuring some aspect of a population of scores.

Answer

parameter

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A parameter is a numerical quantity measuring some aspect of a population of scores.

Original toplevel document

Subject 1. The Nature of Statistics
ve values associated with them, such as the average of all values in a sample and the average of all population values. Values from a population are called parameters, and values from a sample are called statistics. A parameter is a numerical quantity measuring some aspect of a population of scores. The mean, for example, is a measure of central tendency. Greek letters are used to designate parameters. Parameters are rarely known and are usually estimated by statistics computed in samples. Populations can have many parameters, but investment analysts are usually only concerned with a few, such as the mean return or the standard deviation of returns. Estimates of these parameters taken from a sample are called statistics. Much of the field of statistics is devoted to drawing inferences from a sample concerning the value of a population parameter. A statistic is defined as a numerical quantity (such as the mean) calculated in a sample. It has two different meanings. Most commonly, statistics refers to

Flashcard 1332024315148

Tags

#quantitative-methods-basic-concepts #statistics

Question

A parameter is a numerical quantity measuring some aspect of a [...] of scores.

Answer

population

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A parameter is a numerical quantity measuring some aspect of a population of scores.

Original toplevel document

Flashcard 1332040830220

Tags

#quantitative-methods-basic-concepts #statistics

Question

The arithmetic mean is what is commonly called [...]

Answer

the average.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The arithmetic mean is what is commonly called the average.

Original toplevel document

Subject 4. Measures of Center Tendency
; The sample mean is the average for a sample. It is a statistic and is used to estimate the population mean. where n = the number of observations in the sample Arithmetic Mean The arithmetic mean is what is commonly called the average. The population mean and sample mean are both examples of the arithmetic mean. If the data set encompasses an entire population, the arithmetic mean is called a population mean. If the data set includes a sample of values taken from a population, the arithmetic mean is called a sample mean. This is the most widely used measure of central tendency. When the word "mean" is used without a modifier, it can be assumed to refer to the arithmetic mean. The mean is the sum of all scores divided by the number of scores. It is used to measure the prospective (expected future) performance (return) of an investment over a number of periods. All interval and ratio data sets (e.g., incomes, ages, rates of return) have an arithmetic mean. All data values are considered and included in the arithmetic mean computation. A data set has only one arithmetic mean. This indicates that the mean is unique. The arithmetic mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero. Deviation from the arithmetic mean is the distance between the mean and an observation in the data set. The arithmetic mean has the following disadvantages: The mean can be affected by extremes, that is, unusually large or small values. The mean cannot be determined for an open-ended data set (i.e., n is unknown). Geometric Mean The geometric mean has three important properties: It exists only if all the observations are gre

Flashcard 1332043451660

Tags

#quantitative-methods-basic-concepts #statistics

Question

The population mean and sample mean are both examples of the [...]

Answer

arithmetic mean.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The population mean and sample mean are both examples of the arithmetic mean.

Original toplevel document

Flashcard 1332048432396

Tags

#quantitative-methods-basic-concepts #statistics

Question

[...] is the most widely used measure of central tendency.

Answer

the arithmetic mean

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
the arithmetic mean is the most widely used measure of central tendency.

Original toplevel document

Flashcard 1452417355020

Tags

#bayes #programming #r #statistics

Question

After the analysis, we can examine whether the data are well described by the most credible possibilities in the considered set. If the data seem not to be well described, then we can consider expanding the set of possibilities. This process is called a [...]

Answer

posterior predictive check

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
nalysis, we can examine whether the data are well described by the most credible possibilities in the considered set. If the data seem not to be well described, then we can consider expanding the set of possibilities. This process is called a posterior predictive check<body><html>

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452419452172

Tags

#bayes #programming #r #statistics

Question

In general, data analysis begins with a family of candidate descriptions for the data. The descriptions are mathematical formulas that characterize the trends and spreads in the data. The formulas themselves have numbers, called [...], that determine the exact shape of mathematical forms.

Answer

parameter values

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
y>In general, data analysis begins with a family of candidate descriptions for the data. The descriptions are mathematical formulas that characterize the trends and spreads in the data. The formulas themselves have numbers, called parameter values, that determine the exact shape of mathematical forms.<body><html>

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452435967244

Tags

#programming #r #statistics

Question

The first idea is that Bayesian inference is [...]

Answer

reallocation of credibility across possibilities.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The first idea is that Bayesian inference is reallocation of credibility across possibilities.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452437540108

Tags

#bayes #programming #r #statistics

Question

The second foundational idea is that [...]

Answer

the possibilities, over which we allocate credibility, are parameter values in meaningful mathematical models.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The second foundational idea is that the possibilities, over which we allocate credibility, are parameter values in meaningful mathematical models.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452439112972

Tags

#bayes #programming #r #statistics

Question

Why does the population of possiblities always sum to one?

Answer

Because we assume that the candidate causes are mutually exclusive and exhaust all possible causes, the total credibility across causes sums to one.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Because we assume that the candidate causes are mutually exclusive and exhaust all possible causes, the total credibility across causes sums to one.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452443045132

Tags

#bayes #programming #r #statistics

Question

The distribution of credibility initially reflects [...], which can be quite vague. Then new data are observed, and the credibility is re-allocated. Possibilities that are consistent with the data garner more credibility, while possibilities that are not consistent with the data lose credibility.

Answer

prior knowledge about the possibilities

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The distribution of credibility initially reflects prior knowledge about the possibilities, which can be quite vague. Then new data are observed, and the credibility is re-allocated. Possibilities that are consistent with the data garner more credibility, while possibilities

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452445404428

Tags

#bayes #programming #r #statistics

Question

You can think of parameters as [...] on mathematical devices that simulate data generation.

Answer

control knobs

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
You can think of parameters as control knobs on mathematical devices that simulate data generation.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452446977292

Tags

#bayes #programming #r #statistics

Question

You can think of parameters as control knobs on [...].

Answer

mathematical devices that simulate data generation

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
You can think of parameters as control knobs on mathematical devices that simulate data generation.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452448550156

Tags

#bayes #programming #r #statistics

Question

The mathematical formula for the normal distribution converts the parameter values to a particular [...] shape for the probabilities of data values

Answer

bell-like

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The mathematical formula for the normal distribution converts the parameter values to a particular bell-like shape for the probabilities of data values

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452450123020

Tags

#bayes #programming #r #statistics

Question

The second desideratum for a mathematical description is that it should be [...], which means, loosely, that the mathematical form should “look like” the data.

Answer

descrip- tively adequate

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The second desideratum for a mathematical description is that it should be descrip- tively adequate, which means, loosely, that the mathematical form should “look like” the data.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452451695884

Tags

#bayes #programming #r #statistics

Question

The second desideratum for a mathematical description is that it should be descrip- tively adequate, which means, loosely, that the mathematical form should [...] the data.

Answer

“look like”

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The second desideratum for a mathematical description is that it should be descrip- tively adequate, which means, loosely, that the mathematical form should “look like” the data.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452453268748

Tags

#bayes #programming #r #statistics

Question

Bayesian analysis is very useful for assessing the [...] of different candidate descriptions of data

Answer

relative credibility

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Bayesian analysis is very useful for assessing the relative credibility of different candidate descriptions of data

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452454841612

Tags

#bayes #programming #r #statistics

Question

What is the first step in doing bayesian analysis, what questions should be asked?

Answer

Identify the data relevant to the research questions.
What are the measurement scales of the data?
Which data variables are to be predicted
Which data variables are supposed to act as predictors?

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
In general, Bayesian analysis of data follows these steps: 1. Identify the data relevant to the research questions. What are the measurement scales of the data? Which data variables are to be predicted, and which data variables are supposed to act as predictors? 2. Define a descriptive model for the relevant data. The mathematical form and its parameters should be meaningful and appropriate to the theoretical purposes of the analysis. 3. Specif

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452457200908

Tags

#bayes #programming #r #statistics

Question

In bayesian analysis once the data is determined what comes next?

Answer

Define a descriptive model for the relevant data. The mathematical form and its parameters should be meaningful and appropriate to the theoretical purposes of the analysis.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
alysis of data follows these steps: 1. Identify the data relevant to the research questions. What are the measurement scales of the data? Which data variables are to be predicted, and which data variables are supposed to act as predictors? 2. Define a descriptive model for the relevant data. The mathematical form and its parameters should be meaningful and appropriate to the theoretical purposes of the analysis. 3. Specify a prior distribution on the parameters. The prior must pass muster with the audience of the analysis, such as skeptical scientists. 4. Use Bayesian inference to re-allocate c

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452459560204

Tags

#bayes #programming #r #statistics

Question

Once a mathematical model is chosen for bayesian analysis what comes next wrt to the parameters of this model?

Answer

Specify a prior distribution on the parameters. The prior must pass muster with the audience of the analysis, such as skeptical scientists.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
ed, and which data variables are supposed to act as predictors? 2. Define a descriptive model for the relevant data. The mathematical form and its parameters should be meaningful and appropriate to the theoretical purposes of the analysis. 3. Specify a prior distribution on the parameters. The prior must pass muster with the audience of the analysis, such as skeptical scientists. 4. Use Bayesian inference to re-allocate credibility across parameter values. Interpret the posterior distribution with respect to theoretically meaningful issues (assuming that the mod

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452461919500

Tags

#bayes #programming #r #statistics

Question

Once a prior distribution for the parameters is determined what comes next?

Answer

Use Bayesian inference to re-allocate credibility across parameter values. Interpret the posterior distribution with respect to theoretically meaningful issues (assuming that the model is a reasonable description of the data; see next step).

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
its parameters should be meaningful and appropriate to the theoretical purposes of the analysis. 3. Specify a prior distribution on the parameters. The prior must pass muster with the audience of the analysis, such as skeptical scientists. 4. Use Bayesian inference to re-allocate credibility across parameter values. Interpret the posterior distribution with respect to theoretically meaningful issues (assuming that the model is a reasonable description of the data; see next step). 5. Check that the posterior predictions mimic the data with reasonable accuracy (i.e., conduct a “posterior predictive check”). If not, then consider a different descriptive model

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452464278796

Tags

#bayes #programming #r #statistics

Question

What happens if the posterior predictions do not mimic the given data?

Answer

Check that the posterior predictions mimic the data with reasonable accuracy (i.e., conduct a “posterior predictive check”). If not, then consider a different descriptive model

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
e Bayesian inference to re-allocate credibility across parameter values. Interpret the posterior distribution with respect to theoretically meaningful issues (assuming that the model is a reasonable description of the data; see next step). 5. Check that the posterior predictions mimic the data with reasonable accuracy (i.e., conduct a “posterior predictive check”). If not, then consider a different descriptive model<body><html>

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452472929548

Tags

#bayes #programming #r #statistics

Question

One way to summarize the uncertainty is by marking the span of values that are most credible and cover 95% of the distribution. This is called the [...] and is marked by the black bar on the floor of the distribution in Figure 2.5.

Answer

highest density inter val (HDI)

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
One way to summarize the uncertainty is by marking the span of values that are most credible and cover 95% of the distribution. This is called the highest density inter val (HDI) and is marked by the black bar on the floor of the distribution in Figure 2.5.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1452686576908

Tags

#bayes #programming #r #statistics

Question

What does Bayesian analysis do wrt credibility, parameter values and the space of possibilities?

Answer

Bayesian analysis re- allocates credibility among parameter values within a meaningful space of possibilities defined by the chosen model.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Bayesian analysis re- allocates credibility among parameter values within a meaningful space of possibilities defined by the chosen model.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1455233305868

Tags

#bayes #programming #r #statistics

Question

What does the standard deviation control in the normal distribution?

Answer

It controls the width or dispersion of the distribution.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The standard deviation is another control knob in the mathematical formula for the normal distribution that controls the width or dispersion of the distribution. The standard deviation is sometimes called a scale parameter.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1455255325964

Tags

#bayes #programming #r #statistics

Question

What is a disadvantage of resampling or bootsrapping?

Answer

These methods also have very limited ability to express degrees of certainty about characteristics of the data, whereas Bayesian methods put expression of uncertainty front and center

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
o make inferences from data without using a model is a method from NHST called resampling or bootstrapping. These methods compute p values to make decisions, and p values have fundamental logical problems that will be discussed in Chapter 11. These methods also have very limited ability to express degrees of certainty about characteristics of the data, whereas Bayesian methods put expression of uncertainty front and center<body><html>

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1456514141452

Tags

#bayes #programming #r #statistics

Question

The mean is a control knob in the mathematical formula for the normal distribution that controls [...] The mean is sometimes called a location parameter.

Answer

the location of the distribution’s central tendency.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The mean is a control knob in the mathematical formula for the normal distribution that controls the location of the distribution’s central tendency. The mean is sometimes called a location parameter.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1456515714316

Tags

#bayes #programming #r #statistics

Question

The mean is a control knob in the mathematical formula for the normal distribution that controls the location of the distribution’s central tendency. The mean is sometimes called a [...]

Answer

location parameter.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1457076440332

Tags

#bayes #programming #r #statistics

Question

A matrix is simply [...]

Answer

a two-dimensional array of values of the same type.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A matrix is simply a two-dimensional array of values of the same type.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1457142500620

Tags

#bayes #programming #r #statistics

Question

What is a sample space?

Answer

a set of possible outcomes in mind. This set exhausts all possible outcomes, and the outcomes are all mutually exclusive.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Whenever we ask about how likely an outcome is, we always ask with a set of possible outcomes in mind. This set exhausts all possible outcomes, and the outcomes are all mutually exclusive. This set is called the sample space

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1457144859916

Tags

#bayes #programming #r #statistics

Question

What is the technical term for heads in a coin?

Answer

“obverse.”

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Many coins minted by governments have the picture of an important person’s head on one side. This side is called “heads” or, technically, the “obverse.”

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1457186540812

Tags

#bayes #programming #r #statistics

Question

An array is a [...]

Answer

generalization of a matrix to multiple dimensions

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
An array is a generalization of a matrix to multiple dimensions

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1457245785356

Tags

#bayes #programming #r #statistics

Question

One case of trying to make inferences from data without using a model is a method from NHST called [...]

Answer

resampling or bootstrapping.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
One case of trying to make inferences from data without using a model is a method from NHST called resampling or bootstrapping.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1471357259020

Tags

#bayes #programming #r #statistics

Question

In general, a probability, whether it’s outside the head or inside the head, is just a way of [...]

Answer

assigning numbers to a set of mutually exclusive possibilities

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
In general, a probability, whether it’s outside the head or inside the head, is just a way of assigning numbers to a set of mutually exclusive possibilities

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1471358831884

Tags

#bayes #programming #r #statistics

Question

A probability distribution is simply a [...]

Answer

list of all possible outcomes and their corresponding probabilities

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
A probability distribution is simply a list of all possible outcomes and their corresponding probabilities

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1471421746444

Tags

#bayes #programming #r #statistics

Question

For continuous outcome spaces, we can [...] the space into a finite set of mutually exclusive and exhaustive “bins.”

Answer

discretize

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
For continuous outcome spaces, we can discretize the space into a finite set of mutually exclusive and exhaustive “bins.”

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1471423319308

Tags

#bayes #programming #r #statistics

Question

Loosely speaking, the term “mass” refers the amount of stuff in an object. When the stuff is probability and the object is an interval of a scale, then the mass is [...]

Answer

the proportion of the outcomes in the interval.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Loosely speaking, the term “mass” refers the amount of stuff in an object. When the stuff is probability and the object is an interval of a scale, then the mass is the proportion of the outcomes in the interval.

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1471424892172

Tags

#bayes #programming #r #statistics

Question

The problem with using intervals, however, is that [...]. Therefore, what we will do is make the intervals infinitesimally narrow, and instead of talking about the infinitesimal probability mass of each infinitesimal interval, we will talk about the ratio of the probability mass to the interval width. That ratio is called the probability density.

Answer

their widths and edges are arbitrary, and wide intervals are not very precise

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The problem with using intervals, however, is that their widths and edges are arbitrary, and wide intervals are not very precise. Therefore, what we will do is make the intervals infinitesimally narrow, and instead of talking about the infinitesimal probability mass of each infinitesimal interval, we will talk ab

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1471428037900

Tags

#bayes #programming #r #statistics

Question

The problem with using intervals, however, is that their widths and edges are arbitrary, and wide intervals are not very precise. Therefore, what we will do is make the intervals infinitesimally narrow, and instead of talking about the infinitesimal probability mass of each infinitesimal interval, we will talk about the ratio of [...] That ratio is called the probability density.

Answer

the probability mass to the interval width.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
and wide intervals are not very precise. Therefore, what we will do is make the intervals infinitesimally narrow, and instead of talking about the infinitesimal probability mass of each infinitesimal interval, we will talk about the ratio of the probability mass to the interval width. That ratio is called the probability density.<body><html>

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1471429610764

Tags

#bayes #programming #r #statistics

Question

What is probability density?

Answer

The ratio of the probability mass to the interval width, where the width is infinitesamally narrow

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
erefore, what we will do is make the intervals infinitesimally narrow, and instead of talking about the infinitesimal probability mass of each infinitesimal interval, we will talk about the ratio of the probability mass to the interval width. That ratio is called the probability density.<body><html>

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1471506681100

Tags

#bayes #programming #r #statistics

Question

Your job in answering that question is to provide a number between 0 and 1 that accurately reflects your belief probability. One way to come up with such a number is to [...]

Answer

calibrate your beliefs relative to other events with clear probabilities

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Your job in answering that question is to provide a number between 0 and 1 that accurately reflects your belief probability. One way to come up with such a number is to calibrate your beliefs relative to other events with clear probabilities

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1471508253964

Tags

#bayes #programming #r #statistics

Question

The probability of a discrete outcome, such as the probability of falling into an interval on a continuous scale, is referred to as a [...]

Answer

probability mass

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
The probability of a discrete outcome, such as the probability of falling into an interval on a continuous scale, is referred to as a probability mass

Original toplevel document (pdf)

cannot see any pdfs

Flashcard 1641142947084

Tags

#has-images #quantitative-methods-basic-concepts #statistics

Question

The harmonic mean of n numbers x_i (where i = 1, 2, ..., n) is:

X_{H =} [...]

Answer

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on.

Original toplevel document

Subject 4. Measures of Center Tendency
, therefore, is not recommended for use as the only measure of central tendency. A further disadvantage of the mode is that many distributions have more than one mode. These distributions are called "multimodal." Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: The mean, median, and mode are equal in symmetric distributions. The mean is higher than the median in positively skewed distributions and lower than the median in negatively skewed dist

Flashcard 1641160772876

Tags

#has-images #quantitative-methods-basic-concepts #statistics

Question

For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by:

Answer

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
rs x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: <body><html>

Original toplevel document

Flashcard 1641163132172

Tags

#has-images #quantitative-methods-basic-concepts #statistics

Question

The special cases of n = 2 Harmonic Mean

Answer

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mea

Original toplevel document

Flashcard 1641164705036

Tags

#has-images #quantitative-methods-basic-concepts #statistics

Question

The special cases of n = 3 for the Harmonic Mean are given by:

Answer

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Original toplevel document

Flashcard 1645014551820

Tags

#quantitative-methods-basic-concepts #statistics

Question

Is the Geometric mean and Geometric mean returns calculated the same way?

Answer

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on.

Original toplevel document

Flashcard 1645933628684

Tags

#statistics

Question

A statistical question requires [...]

Answer

collecting data with variability

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Flashcard 3111646792972

Tags

#deeplearning #embeddings #nlp

Question

What are categorical embeddings?

Answer

To map the categorical variables in a function approximation problem into Euclidean spaces, i.e. transform the categorical features into an array in a d dimensional space.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 3111649152268

Tags

#deeplearning #embeddings #nlp

Question

List three reasons to use Entity Embeddings of categorical variables.

Answer

Entity embedding reduces memory usage
It speeds up neural networks training compared with one-hot encoding,
More importantly by mapping similar values close to each other in the embedding space it reveals the intrinsic properties of the categorical variables

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 3111650987276

Tags

#deeplearning #embeddings #nlp

Question

What EDA and step is made possible with Entity Embeddings of Categorical Variables, otherwise only meaningfull with Numerical Features?

Answer

As entity embedding defines a distance measure for categorical variables it can be used for visualizing categorical data and for data clustering.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 3126364605708

Tags

#deeplearning #embeddings #nlp

Question

What is the main difficulty in applying neural networks to Structured Data?

Answer

Neural Networks maps the features to some continuous function.
Unlike unstructured data found in nature, structured data with categorical features may not have continuity at all and even if it has it may not be so obvious

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 3126366440716

Tags

#deeplearning #embeddings #nlp

Question

Describe 2 shortcomings in using one-hot encoding of Categorical Variables

Answer

When we have many high cardinality features one-hot encoding often results in an unrealistic amount of computational resource requirement.
It treats different values of categorical variables completely independent of each other and often ignores the informative relations between them.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 3963046464780

Tags

#background #deeplearning

Question

In the last few years, we have witnessed tremendous improvements in recognition performance, mainly due to advances in two technical directions:

Answer

building more powerful models
designing effective strategies against overfitting.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 4009031765260

Tags

#deeplearning #initialization

Question

After the success of CNNs in IVSRC 2012 (Krizhevsky et al. (2012)), initialization with Gaussian noise with mean equal to zero and standard deviation set to 0.01 and adding bias equal to one for some layers become very popular.

Why it is not possible to train very deep networks from scratch with this initialization?

Answer

[default - edit me]

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 4028512472332

Tags

#deeplearning #fastai #initialization #kaiming #lesson_8

Question

Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification

What is about?

Answer

This paper introduced a successful method for initializing Neural Networks which use non-linear functions such as Relu, called here rectifiers.

As the title says, the performance made it possible to surpass human-level performance on Imagenet.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 4028517977356

Tags

#deeplearning #fastai #has-images #initialization #kaiming #lesson_8

The convergence of a 22-layer large model. We use ReLU as the activation for both cases. Both our initialization (red) and “Xavier” (blue) [7] lead to convergence, but ours starts reducing error earlier.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

pdf

cannot see any pdfs

Flashcard 4344775576844

Question

When you pass a tuple as the first argument in an [...] statement, the [...] always evaluates as true and therefore never fails.

Answer

assert, assertion

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
When you pass a tuple as the first argument in an assert statement, the assertion always evaluates as true and therefore never fails.

Original toplevel document

Assert Statements in Python – dbader.org
valuate to true. I’ve been bitten by this myself in the past. I wrote a longer article about this specific issue you can check out by clicking here. Alternatively, here’s the executive summary: When you pass a tuple as the first argument in an assert statement, the assertion always evaluates as true and therefore never fails. For example, this assertion will never fail: assert(1 == 2, 'This should fail') This has to do with non-empty tuples always being truthy in Python. If you pass a tuple to an assert stat

Flashcard 4344779509004

Question

When you pass a tuple as the first argument in an [...] statement, the [...] always evaluates as true and therefore never fails.

Answer

assert, assertion

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
When you pass a tuple as the first argument in an assert statement, the assertion always evaluates as true and therefore never fails.

Original toplevel document

Annotation 4345010457868

Наука, изучающая сон, называется сомнология, сновидения — онейрология.

status	not read	reprioritisations
last reprioritisation on		suggested re-reading day
started reading on		finished reading on

Сновидение — Википедия
идений 2.1 По З. Фрейду 2.2 Толкование сновидений К. Юнга 3 «Управление» сновидениями 4 Сновидение в религии 5 Дежавю 6 См. также 7 Примечания 8 Литература Общие сведения[править | править код] Наука, изучающая сон, называется сомнология, сновидения — онейрология. Сновидения считаются связанными с фазой быстрого движения глаз (БДГ). Эта стадия возникает примерно каждые 1,5—2 часа сна, и её продолжительность постепенно удлиняется. Она характеризуе

Flashcard 4345012030732

Question

Наука, изучающая сон, называется [...] сновидения — онейрология.

Answer

сомнология,

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Наука, изучающая сон , называется сомнология , сновидения — онейрология .

Original toplevel document

Flashcard 4345013603596

Question

Наука, изучающая сон, называется сомнология, сновидения — [...]

Answer

онейрология.

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

Parent (intermediate) annotation

Open it
Наука, изучающая сон , называется сомнология , сновидения — онейрология .

Original toplevel document

Annotation 4345020943628

B, P{A\ B) is the fraction that is assigned to possible outcomes that also belong to A

status	not read	reprioritisations
last reprioritisation on		suggested re-reading day
started reading on		finished reading on

pdf

cannot see any pdfs

Edited, memorised or added to reading queue

on 24-Aug-2019 (Sat)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

pdf

pdf

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document (pdf)

Parent (intermediate) annotation

Original toplevel document

Parent (intermediate) annotation

Original toplevel document

Parent (intermediate) annotation

Original toplevel document

Parent (intermediate) annotation

Original toplevel document

Parent (intermediate) annotation

Original toplevel document

Parent (intermediate) annotation

Original toplevel document

Parent (intermediate) annotation

Original toplevel document