Editing Statistical inference (section)

== Introduction ==
Statistical inference makes propositions about a population, using data drawn from the population with some form of [[Sampling (statistics)|sampling]]. Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) [[Model selection|selecting]] a [[statistical model]] of the process that generates the data and (second) deducing propositions from the model.<ref>{{cite web|last=Johnson|first=Richard|title=Statistical Inference|website=Encyclopedia of Mathematics|publisher=Springer: The European Mathematical Society|date=12 March 2016|url=https://encyclopediaofmath.org/wiki/Statistical_inference|access-date=26 October 2022}}</ref>

Konishi and Kitagawa state "The majority of the problems in statistical inference can be considered to be problems related to statistical modeling".<ref>Konishi & Kitagawa (2008), p. 75.</ref> Relatedly, [[David Cox (statistician)|Sir David Cox]] has said, "How [the] translation from subject-matter problem to statistical model is done is often the most critical part of an analysis".<ref>Cox (2006), p. 197.</ref>

The [[Logical consequence|conclusion]] of a statistical inference is a statistical [[proposition]].<ref>{{Cite web |url = https://www.encyclopediaofmath.org/index.php/Statistical_inference |title=Statistical inference - Encyclopedia of Mathematics |website=www.encyclopediaofmath.org |access-date=2019-01-23 }}</ref> Some common forms of statistical proposition are the following:
* a [[point estimate]], i.e. a particular value that best approximates some parameter of interest;
* an [[interval estimate]], e.g. a [[confidence interval]] (or set estimate), i.e. an interval constructed using a dataset drawn from a population so that, under repeated sampling of such datasets, such intervals would contain the true parameter value with the [[frequency probability|probability]] at the stated [[confidence level]];
* a [[credible intervals|credible interval]], i.e. a set of values containing, for example, 95% of posterior belief;
* rejection of a [[statistical hypothesis testing|hypothesis]];{{NoteTag|According to Peirce, acceptance means that inquiry on this question ceases for the time being. In science, all scientific theories are revisable.}}
* [[Cluster analysis|clustering]] or [[Statistical classification|classification]] of data points into groups.