Editing Bayesian inference (section)

===Model selection===
{{main|Bayesian model selection}}
{{see also|Bayesian information criterion}}
Bayesian methodology also plays a role in [[model selection]] where the aim is to select one model from a set of competing models that represents most closely the underlying process that generated the observed data. In Bayesian model comparison, the model with the highest [[posterior probability]] given the data is selected. The posterior probability of a model depends on the evidence, or [[marginal likelihood]], which reflects the probability that the data is generated by the model, and on the [[Prior probability|prior belief]] of the model. When two competing models are a priori considered to be equiprobable, the ratio of their posterior probabilities corresponds to the [[Bayes factor]]. Since Bayesian model comparison is aimed on selecting the model with the highest posterior probability, this methodology is also referred to as the maximum a posteriori (MAP) selection rule <ref>{{cite journal|first1= P.|last1= Stoica |first2 = Y.|last2 =Selen|journal = IEEE Signal Processing Magazine |date = 2004| title = A review of information criterion rules|doi=10.1109/MSP.2004.1311138|volume=21|issue=4|pages=36–47|s2cid= 17338979 }}</ref> or the MAP probability rule.<ref>{{cite journal|first1= J.|last1= Fatermans |first2 = S.|last2 =Van Aert |first3=A.J. |last3=den Dekker|journal = Ultramicroscopy |date = 2019|title = The maximum a posteriori probability rule for atom column detection from HAADF STEM images|doi=10.1016/j.ultramic.2019.02.003|volume=201|pages=81–91|pmid= 30991277 |arxiv=1902.05809| s2cid= 104419861 }}</ref>