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#### 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= [...] .
Answer
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

Tags
#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 .
Answer
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

Tags
#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 .
Answer
an additive

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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

Tags
#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 = [...] .
Answer
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

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

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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

Tags
#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, ....
Answer
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 = [...].
Answer
... 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

Tags
#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 )
Answer
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 )
Answer
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

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 Yt = [...]
Answer
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

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

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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 $$\hat{m_t}$$
Answer
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.
Answer
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.
Answer
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.
Answer
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 [...].
Answer
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.
Answer
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 [...].
Answer
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.
Answer
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?
Answer
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?
Answer
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 [...]
Answer
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 [...].
Answer
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.
Answer
$$\hat{x}_{n+1}$$ = 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.
Answer
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.
Answer
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.
Answer
additive

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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.
Answer
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.
Answer
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.
Answer
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.
Answer
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

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#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 [...].
Answer
$$\hat{x}_1$$ = 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)$$\hat{x}_n$$
Answer
expanded m-times is
$$\large \hat{x}_{n+1} = \sum_{i=0}^m\alpha(1-\alpha)^ix_{n-i}+(1-\alpha)^{m+1}\hat{x}_{n-m}$$

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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.
Answer
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

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

#### Flashcard 1332022742284

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

#### Flashcard 1332024315148

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

#### Flashcard 1332040830220

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

#### Flashcard 1332043451660

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

#### Flashcard 1332048432396

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#quantitative-methods-basic-concepts #statistics
Question
[...] is the most widely used measure of central tendency.
Answer
the arithmetic mean

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

#### 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 <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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#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

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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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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

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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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#programming #r #statistics
Question
The first idea is that Bayesian inference is [...]
Answer
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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Question
The second foundational idea is that [...]
Answer
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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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.

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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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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

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

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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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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

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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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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”

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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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#### Flashcard 1452453268748

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

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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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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.

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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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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.

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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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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).

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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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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

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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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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)

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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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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.

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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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What does the standard deviation control in the normal distribution?
Answer
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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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

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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.
Answer
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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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.

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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 [...]
Answer
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?
Answer
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?
Answer
“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 [...]
Answer
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 [...]
Answer
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 [...]
Answer
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 [...]
Answer
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.”
Answer
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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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.

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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.
Answer
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.
Answer
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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Question
What is probability density?
Answer
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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#### Flashcard 1471506681100

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#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 [...]
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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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#bayes #programming #r #statistics
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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 [...]
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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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#### Flashcard 1641142947084

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

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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 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

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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 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?
Answer
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.

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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 1645933628684

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

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#### Flashcard 3111646792972

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#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.

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#deeplearning #embeddings #nlp
Question
List three reasons to use Entity Embeddings of categorical variables.
Answer
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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#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?
Answer
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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#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

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#deeplearning #embeddings #nlp
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Describe 2 shortcomings in using one-hot encoding of Categorical Variables
Answer
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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#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:
Answer
1. building more powerful models
2. designing effective strategies against overfitting.

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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?

Answer
[default - edit me]

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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

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.

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

#### Annotation 4345010457868

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

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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 .

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