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

Question

Consider the multiplicative model X_{t} = m_{t} × s_{t} × W_{t} .Let Y_{t} denote the time series of logarithms: Y_{t} =log X_{t} .Then

- Y
_{t}=log X_{t} - Y
_{t}= log(m_{t}× s_{t}× W_{t}) - Y
_{t}= [...] .

Answer

log m_{t} +log s_{t} +log W_{t}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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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Question

if a [...] model is appropriate for the time series X_{t} , then an additive model is appropriate for the time series of logarithms, Y_{t} =log X_{t} .

Answer

multiplicative

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 .

Tags

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

Question

if a multiplicative model is appropriate for the time series X_{t} , then [...] model is appropriate for the time series of logarithms, Y_{t} =log X_{t} .

Answer

an additive

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 .

Tags

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

Question

if a multiplicative model is appropriate for the time series X_{t} , then an additive model is appropriate for the time series of logarithms, Y_{t} = [...] .

Answer

log X_{t}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 .

Tags

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

Question

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

Answer

taking logarithms

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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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Question

Transformations of time series that are commonly used include the power transformations:

Y_{t} = [...] , where a = ... 1/4, 1/3, 1/2, 2, 3, 4, ....

Y

Answer

X_{t}^{a}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Question

Transformations of time series that are commonly used include the power transformations:

Y_{t} = X_{t}^{a} , where a = [...].

Y

Answer

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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, ....

Tags

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

Question

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

Answer

simple moving average (or just a moving average)

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Question

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

Answer

order (or span)

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 )

Tags

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

Question

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

Answer

Y_{t }= \(\large \frac{1}{11}\)(X_{t−5} + ···+ X_{t} + ···+ X_{t+5} )

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 )

Tags

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

Question

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

Answer

centred

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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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Question

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

Answer

an estimate

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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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Question

A [...] 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.

MA(t)= a

where the weights a

Answer

weighted

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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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Question

A weighted moving average of order [...] 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.

MA(t)= a

where the weights a

Answer

2q + 1

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Question

A weighted moving average of order 2q + 1 has the form

MA(t)=_{[...]} ,

where the weights a_{j} , j = −q, −q +1,... ,q, add up to 1.

MA(t)=

where the weights a

Answer

a_{−q} X_{t−q} + ···+ a_{−1} X_{t−1} + a_{0} X_{t} + a_{1} X_{t+1} + ···+ a_{q} X_{t+q}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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.

Tags

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

Question

A weighted moving average of order 2q + 1 has the form

MA(t)= a_{−q} X_{t−q} + ···+ a_{−1} X_{t−1} + 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 [...].

MA(t)= a

where the weights a

Answer

1

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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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Question

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

Answer

SA(t)

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Tags

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Question

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

Answer

seasonal variation

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Tags

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

Question

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

Answer

the period T of the seasonal cycle

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

scheduled repetition interval | last repetition or drill |

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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Question

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

Answer

No, the period is an even number.

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Tags

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

Question

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

Answer

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Tags

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

Question

The simple moving average is a weighted moving average in which the weights a_{j} are all equal to [...]

Answer

N^{ −1}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Tags

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

Question

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

Answer

today’s

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Tags

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

Question

If a time series X_{t} is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula

\(\hat{x}_{n+1}\) =**[...]**

where:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) =

where:

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

Answer

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Tags

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

Question

If a time series X_{t} is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula

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

where:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) = αx

where:

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

Answer

the 1-step ahead forecasts of X_{n} and X_{n+1},

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

t level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \hat{x}_nand \hat{x}_{n+1}are <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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#m249 #mathematics #open-university #statistics #time-series

Question

If a time series X_{t} is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula

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

where:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) = αx

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 [...].

Answer

a smoothing parameter, 0 ≤ α ≤ 1

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

e obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \hat{x}_nand \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n+1 , and α is <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>

Tags

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

Question

If a time series X_{t} is described by an [...] model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula

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

where:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) = αx

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.

Answer

additive

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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:&

Tags

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

Question

If a time series X_{t} is described by an additive model with [...] level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula

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

where:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) = αx

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.

Answer

constant

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Tags

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

Question

If a time series X_{t} is described by an additive model with constant level and [...] seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula

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

where:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) = αx

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.

Answer

no

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Tags

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

Question

If a time series X_{t} is described by an additive model with constant level and no seasonality, [...]-step ahead forecasts may be obtained by simple exponential smoothing using the formula

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

where:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) = αx

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.

Answer

1

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Tags

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

Question

If a time series X_{t} is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple [...] using the formula

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

where:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) = αx

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.

Answer

exponential smoothing

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Tags

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

Question

If a time series X_{t} is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula

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

where:**[...]**.

\(\hat{x}_{n+1}\) = αx

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.

Answer

\(\hat{x}_1\) = x_{1}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Tags

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Question

what does the expanded **m-times **(i.e. non recursive) simple exponential smoothing formula looks like?

fully recursive is:

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

fully recursive is:

\(\hat{x}_{n+1}\)= αx

Answer

expanded m-times is

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

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

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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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Question

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

Answer

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

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

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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.

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

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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)

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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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.

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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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.

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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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.

; 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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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.

; 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

Tags

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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.

; 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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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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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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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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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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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?

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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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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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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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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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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Question

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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Question

What is a disadvantage of resampling or bootsrapping?

Answer

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

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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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Question

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

Answer

the location of the distribution’s central tendency.

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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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Question

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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Question

What is a sample space?

Answer

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

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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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Question

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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Question

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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Question

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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scheduled repetition interval | last repetition or drill |

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

Tags

#bayes #programming #r #statistics

Question

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

Answer

assigning numbers to a set of mutually exclusive possibilities

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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

Tags

#bayes #programming #r #statistics

Question

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

Tags

#bayes #programming #r #statistics

Question

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

Answer

discretize

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

Tags

#bayes #programming #r #statistics

Question

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

Answer

the proportion of the outcomes in the interval.

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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.

Tags

#bayes #programming #r #statistics

Question

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

Answer

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

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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

Tags

#bayes #programming #r #statistics

Question

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

Answer

the probability mass to the interval width.

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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>

Tags

#bayes #programming #r #statistics

Question

What is probability density?

Answer

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

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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>

Tags

#bayes #programming #r #statistics

Question

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

Answer

calibrate your beliefs relative to other events with clear probabilities

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scheduled repetition interval | last repetition or drill |

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

Tags

#bayes #programming #r #statistics

Question

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

Answer

probability mass

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scheduled repetition interval | last repetition or drill |

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

Tags

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

Question

The **harmonic mean** of n numbers x_{i} (where i = 1, 2, ..., n) is:

X_{H = } **[...]**

Answer

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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.

, 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

Tags

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

Question

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

Answer

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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>

, 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

Tags

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

Question

The special cases of n = 2 **Harmonic Mean**

Answer

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

scheduled repetition interval | last repetition or drill |

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

, 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

Tags

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

Question

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

Answer

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

, 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

Tags

#quantitative-methods-basic-concepts #statistics

Question

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

Answer

No

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

scheduled repetition interval | last repetition or drill |

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.

, 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

Tags

#statistics

Question

A statistical question requires **[...]**

Answer

collecting data with variability

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Tags

#deeplearning #embeddings #nlp

Question

What are categorical embeddings?

Answer

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

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Tags

#deeplearning #embeddings #nlp

Question

List three reasons to use Entity Embeddings of categorical variables.

Answer

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

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Tags

#deeplearning #embeddings #nlp

Question

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

Answer

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

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Tags

#deeplearning #embeddings #nlp

Question

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

Answer

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

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scheduled repetition interval | last repetition or drill |

Tags

#deeplearning #embeddings #nlp

Question

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

Answer

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

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Tags

#background #deeplearning

Question

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

Answer

- building more powerful models
- designing effective strategies against overfitting.

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Tags

#deeplearning #initialization

Question

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

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

Answer

[default - edit me]

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Tags

#deeplearning #fastai #initialization #kaiming #lesson_8

Question

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

What is about?

Answer

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

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

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Tags

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

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Question

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

`[...]`

statement, the 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.

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

Question

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

`[...]`

statement, the Answer

assert, assertion

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

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

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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

Question

Answer

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

scheduled repetition interval | last repetition or drill |

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

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

Question

Answer

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

scheduled repetition interval | last repetition or drill |

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

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

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

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