on 24-Aug-2019 (Sat)

Flashcard 150890360

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#m249 #mathematics #open-university #statistics #time-series
Question
Consider the multiplicative model Xt = mt × st × Wt .Let Yt denote the time series of logarithms: Yt =log Xt .Then
• Yt =log Xt
• Yt= log(mt × st × Wt)
• Yt= [...] .
log mt +log st +log Wt

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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 .

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Flashcard 150890373

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#m249 #mathematics #open-university #statistics #time-series
Question
if a [...] model is appropriate for the time series Xt , then an additive model is appropriate for the time series of logarithms, Yt =log Xt .
multiplicative

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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 .

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Flashcard 150890379

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#m249 #mathematics #open-university #statistics #time-series
Question
if a multiplicative model is appropriate for the time series Xt , then [...] model is appropriate for the time series of logarithms, Yt =log Xt .

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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 .

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Flashcard 150890385

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#m249 #mathematics #open-university #statistics #time-series
Question
if a multiplicative model is appropriate for the time series Xt , then an additive model is appropriate for the time series of logarithms, Yt = [...] .
log Xt

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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 .

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Flashcard 150890398

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#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.
taking logarithms

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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.

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Flashcard 150890411

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#m249 #mathematics #open-university #statistics #time-series
Question
Transformations of time series that are commonly used include the power transformations:
Yt = [...] , where a = ... 1/4, 1/3, 1/2, 2, 3, 4, ....
Xta

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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, ....

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Flashcard 150890417

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
Transformations of time series that are commonly used include the power transformations:
Yt = Xta , where a = [...].
... 1/4, 1/3, 1/2, 2, 3, 4, ...

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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, ....

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Flashcard 150890430

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#m249 #mathematics #open-university #statistics #time-series
Question
A [...] of order (or span) 11 can be written as Yt = $$\large \frac{1}{11}$$(Xt−5 + ···+ Xt + ···+ Xt+5 )
simple moving average (or just a moving average)

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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 )

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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 Yt = $$\large \frac{1}{11}$$(Xt−5 + ···+ Xt + ···+ Xt+5 )
order (or span)

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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 )

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Flashcard 150890442

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#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 Yt = [...]
Yt = $$\large \frac{1}{11}$$(Xt−5 + ···+ Xt + ···+ Xt+5 )

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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 )

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Flashcard 150890455

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#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.
centred

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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.

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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 mt ; this is denoted $$\hat{m_t}$$
an estimate

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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^

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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 Xt−q + ···+ a−1 Xt−1 + a0 Xt + a1 Xt+1 + ···+ aq Xt+q ,
where the weights aj , j = −q, −q +1,... ,q, add up to 1.
weighted

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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,... ,

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Flashcard 150890565

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
A weighted moving average of order [...] has the form
MA(t)= a−q Xt−q + ···+ a−1 Xt−1 + a0 Xt + a1 Xt+1 + ···+ aq Xt+q ,
where the weights aj , j = −q, −q +1,... ,q, add up to 1.
2q + 1

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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.</

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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 aj , j = −q, −q +1,... ,q, add up to 1.
a−q Xt−q + ···+ a−1 Xt−1 + a0 Xt + a1 Xt+1 + ···+ aq Xt+q

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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.

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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 Xt−q + ···+ a−1 Xt−1 + a0 Xt + a1 Xt+1 + ···+ aq Xt+q ,
where the weights aj , j = −q, −q +1,... ,q, add up to [...].
1

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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>

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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.
SA(t)

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

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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 [...].
seasonal variation

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

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Flashcard 150890609

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
The ﬁrst step is to ﬁnd an initial estimate of the trend component mt that is not unduly inﬂuenced by the seasonal component st. 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.
the period T of the seasonal cycle

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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>

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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?
No, the period is an even number.

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

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Flashcard 150890643

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
The simple moving average is a weighted moving average in which the weights aj are all equal to [...]
N −1

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

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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 [...].
today’s

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

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Flashcard 150890996

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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.
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$

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Flashcard 150891005

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn 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.
the 1-step ahead forecasts of Xn and Xn+1,

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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}_n​and \hat{x}_{n+1}are <span>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 .<span><body><html>

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Flashcard 150891011

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+1,
• and α is [...].
The method requires an initial value $$\hat{x}_1$$, which is often chosen to be x1 : $$\hat{x}_1$$ = x1.
a smoothing parameter, 0 ≤ α ≤ 1

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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}_n​and \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n+1 , and α is <span>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 .<span><body><html>

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Flashcard 150891017

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$ and $$\hat{x}_{n+1}$$ are the 1-step ahead forecasts of Xn and Xn+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.

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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:&

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Flashcard 150891023

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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.
constant

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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 ob

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Flashcard 150891029

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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.
no

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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

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Flashcard 150891035

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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.
1

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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, \ha

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Flashcard 150891041

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple [...] using the formula
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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.
exponential smoothing

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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}_n​and \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n

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Flashcard 150891047

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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 [...].
$$\hat{x}_1$$ = x1

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Flashcard 150891359

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#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:

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

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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.

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Flashcard 1332009897228

Tags
#quantitative-methods-basic-concepts #statistics
Question
A [...] is defined as a numerical quantity (such as the mean) calculated in a sample.
statistic

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

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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. <span>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 [...]
sample.

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

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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. <span>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 1332018023692

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#quantitative-methods-basic-concepts #statistics
Question
the order of the different scales is [...]
NOIR (the French word for black)

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

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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. <span>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

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

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

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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. <span>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

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

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

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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. <span>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

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

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The arithmetic mean is what is commonly called the average.

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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 <span>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

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

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

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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 <span>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

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

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

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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 <span>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 1452417355020

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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 [...]
posterior predictive check

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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 <span>posterior predictive check<span><body><html>

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Flashcard 1452419452172

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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.
parameter values

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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>

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Flashcard 1452435967244

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The first idea is that Bayesian inference is [...]
reallocation of credibility across possibilities.

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

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

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

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Why does the population of possiblities always sum to one?
Because we assume that the candidate causes are mutually exclusive and exhaust all possible causes, the total credibility across causes sums to one.

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

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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.

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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

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Flashcard 1452445404428

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

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

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Flashcard 1452446977292

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

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

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Flashcard 1452448550156

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

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

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

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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.

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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.
“look like”

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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.

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

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

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Flashcard 1452454841612

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

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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

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Flashcard 1452457200908

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

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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. <span>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

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Flashcard 1452459560204

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Once a mathematical model is chosen for bayesian analysis what comes next wrt to the parameters of this model?
Specify a prior distribution on the parameters. The prior must pass muster with the audience of the analysis, such as skeptical scientists.

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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. <span>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

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Flashcard 1452461919500

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

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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. <span>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

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

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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. <span>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<span><body><html>

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Flashcard 1452472929548

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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.
highest density inter val (HDI)

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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.

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Flashcard 1452686576908

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What does Bayesian analysis do wrt credibility, parameter values and the space of possibilities?
Bayesian analysis re- allocates credibility among parameter values within a meaningful space of possibilities defined by the chosen model.

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

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Flashcard 1455233305868

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What does the standard deviation control in the normal distribution?
It controls the width or dispersion of the distribution.

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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.

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Flashcard 1455255325964

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What is a disadvantage of resampling or bootsrapping?
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

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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. <span>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<span><body><html>

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

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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.

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Flashcard 1456515714316

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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.

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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.

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A matrix is simply [...]
a two-dimensional array of values of the same type.

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

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Flashcard 1457142500620

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What is a sample space?
a set of possible outcomes in mind. This set exhausts all possible outcomes, and the outcomes are all mutually exclusive.

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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

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What is the technical term for heads in a coin?
“obverse.”

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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.”

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An array is a [...]
generalization of a matrix to multiple dimensions

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An array is a generalization of a matrix to multiple dimensions

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

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

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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

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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

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A probability distribution is simply a [...]
list of all possible outcomes and their corresponding probabilities

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

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

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

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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.

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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.

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

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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

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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.
the probability mass to the interval width.

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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 <span>the probability mass to the interval width. That ratio is called the probability density.<span><body><html>

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

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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. <span>That ratio is called the probability density.<span><body><html>

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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

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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

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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

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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

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

XH = [...]

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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.

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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." <span>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

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#has-images #quantitative-methods-basic-concepts #statistics
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For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by:

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

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." <span>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 1641163132172

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#has-images #quantitative-methods-basic-concepts #statistics
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The special cases of n = 2 Harmonic Mean

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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

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." <span>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 1641164705036

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#has-images #quantitative-methods-basic-concepts #statistics
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The special cases of n = 3 for the Harmonic Mean are given by:

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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

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." <span>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 1645014551820

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#quantitative-methods-basic-concepts #statistics
Question
Is the Geometric mean and Geometric mean returns calculated the same way?
No

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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." <span>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 1645933628684

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#statistics
Question
A statistical question requires [...]
collecting data with variability

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Flashcard 3111646792972

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#deeplearning #embeddings #nlp
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What are categorical embeddings?
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.

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Flashcard 3111649152268

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#deeplearning #embeddings #nlp
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List three reasons to use Entity Embeddings of categorical variables.
1. Entity embedding reduces memory usage
2. ​​It speeds up neural networks training compared with one-hot encoding,
3. More importantly by mapping similar values close to each other in the embedding space it reveals the intrinsic properties of the categorical variables

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Flashcard 3111650987276

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#deeplearning #embeddings #nlp
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What EDA and step is made possible with Entity Embeddings of Categorical Variables, otherwise only meaningfull with Numerical Features?
As entity embedding defines a distance measure for categorical variables it can be used for visualizing categorical data and for data clustering.

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Flashcard 3126364605708

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#deeplearning #embeddings #nlp
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What is the main difficulty in applying neural networks to Structured Data?
• 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

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Flashcard 3126366440716

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#deeplearning #embeddings #nlp
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Describe 2 shortcomings in using one-hot encoding of Categorical Variables
1. When we have many high cardinality features one-hot encoding often results in an unrealistic amount of computational resource requirement.
2. It treats different values of categorical variables completely independent of each other and often ignores the informative relations between them.

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Flashcard 3963046464780

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#background #deeplearning
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In the last few years, we have witnessed tremendous improvements in recognition performance, mainly due to advances in two technical directions:
1. building more powerful models
2. designing effective strategies against overfitting.

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Flashcard 4009031765260

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#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?

[default - edit me]

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Flashcard 4028512472332

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#deeplearning #fastai #initialization #kaiming #lesson_8
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Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification

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.

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Flashcard 4028517977356

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#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.

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Flashcard 4344775576844

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

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

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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: <span>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

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

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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: <span>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

Annotation 4345010457868

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

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] <span>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

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

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

Original toplevel document

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] <span>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

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

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

Original toplevel document

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] <span>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

Annotation 4345020943628

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