# Difference between revisions of "Statistical Inference"

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− | A [[Statistical Inference]] is a [[data-driven inference]] in the form of a [[statistical statement]]. | + | A [[Statistical Inference]] is a [[data-driven inference]] (about the properties of an underlying [[probability distribution]]) in the form of a [[statistical statement]]. |

* <B>Context:</B> | * <B>Context:</B> | ||

** It can be produced by a [[Statistical Inference System]] (solving a [[statistical inference task]]). | ** It can be produced by a [[Statistical Inference System]] (solving a [[statistical inference task]]). | ||

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** a [[Logical Inference]]. | ** a [[Logical Inference]]. | ||

** a [[Descriptive Statistic]], such as [[central tendency]]. | ** a [[Descriptive Statistic]], such as [[central tendency]]. | ||

− | * <B>See:</B> [[Predicted Number]], [[Causal Inference]], [[Statistical Regression]]. | + | * <B>See:</B> [[Inductive Inference]], [[Predicted Number]], [[Causal Inference]], [[Statistical Regression]], [[Descriptive Statistics]], [[Data Analysis]], [[Probability Distribution]], [[Statistical Population]], [[Sampling (Statistics)]]. |

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− | == References == | + | ==References== |

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+ | === 2019 === | ||

+ | * (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/statistical_inference Retrieved:2019-6-14. | ||

+ | ** '''Statistical inference''' is the process of using [[data analysis]] to deduce properties of an underlying [[probability distribution]]. Inferential statistical analysis infers properties of a [[Statistical population|population]], for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is [[Sampling (statistics)|sampled]] from a larger population. <P> Inferential statistics can be contrasted with [[descriptive statistics]]. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. | ||

=== 2017 === | === 2017 === | ||

* Digio (https://stats.stackexchange.com/users/83065/digio), Differences between logistic regression and perceptrons, URL (version: 2017-06-07): https://stats.stackexchange.com/q/284013 | * Digio (https://stats.stackexchange.com/users/83065/digio), Differences between logistic regression and perceptrons, URL (version: 2017-06-07): https://stats.stackexchange.com/q/284013 | ||

** QUOTE: ... Long story short, [[logistic regression]] is a [[GLM]] which can perform [[data-driven prediction|prediction]] and [[Statistical Inference|inference]], whereas the [[linear Perceptron]] can only achieve prediction (in which case it will perform the same as [[logistic regression]]). The difference between the two is also the fundamental difference between [[statistical modelling]] and [[machine learning]]. | ** QUOTE: ... Long story short, [[logistic regression]] is a [[GLM]] which can perform [[data-driven prediction|prediction]] and [[Statistical Inference|inference]], whereas the [[linear Perceptron]] can only achieve prediction (in which case it will perform the same as [[logistic regression]]). The difference between the two is also the fundamental difference between [[statistical modelling]] and [[machine learning]]. | ||

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=== 2002 === | === 2002 === |

## Revision as of 08:11, 14 June 2019

A Statistical Inference is a data-driven inference (about the properties of an underlying probability distribution) in the form of a statistical statement.

**Context:**- It can be produced by a Statistical Inference System (solving a statistical inference task).
- It involves Statistical Hypothesis Testing and Statistical Modelling.

**Example(s):****Counter-Example(s):****See:**Inductive Inference, Predicted Number, Causal Inference, Statistical Regression, Descriptive Statistics, Data Analysis, Probability Distribution, Statistical Population, Sampling (Statistics).

## References

### 2019

- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/statistical_inference Retrieved:2019-6-14.
**Statistical inference**is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.

### 2017

- Digio (https://stats.stackexchange.com/users/83065/digio), Differences between logistic regression and perceptrons, URL (version: 2017-06-07): https://stats.stackexchange.com/q/284013
- QUOTE: ... Long story short, logistic regression is a GLM which can perform prediction and inference, whereas the linear Perceptron can only achieve prediction (in which case it will perform the same as logistic regression). The difference between the two is also the fundamental difference between statistical modelling and machine learning.

### 2002

- (Garthwaite et al., 2002) ⇒ Paul Garthwaite, Ian Jolliffe, Byron Jones. (2002). “Statistical Inference, 2nd edition." Oxford University Press. ISBN:0-19-857226-3
- QUOTE: Adopting a broad view of statistical inference, the text concentrates on what various techniques do, with mathematical proof kept to a minimum. The approach is rigorous but accessible to final year undergraduates. Classical approaches to point estimation, hypothesis testing and interval estimation are all covered thoroughly with recent developments outlined.

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