Editing Bayesian statistics (section)

===Exploratory analysis of Bayesian models===

Exploratory analysis of Bayesian models is an adaptation or extension of the [[exploratory data analysis]] approach to the needs and peculiarities of Bayesian modeling. In the words of Persi Diaconis:<ref>Diaconis, Persi (2011) Theories of Data Analysis: From Magical Thinking Through Classical Statistics. John Wiley & Sons, Ltd 2:e55 {{doi|10.1002/9781118150702.ch1}}</ref> 
{{Quote|Exploratory data analysis seeks to reveal structure, or simple descriptions in data. We look at numbers or graphs and try to find patterns. We pursue leads suggested by background information, imagination, patterns perceived, and experience with other data analyses}}

The [[Bayesian inference|inference process]] generates a posterior distribution, which has a central role in Bayesian statistics, together with other distributions like the posterior predictive distribution and the prior predictive distribution. The correct visualization, analysis, and interpretation of these distributions is key to properly answer the questions that motivate the inference process.<ref>{{cite journal |doi=10.21105/joss.01143 |title=ArviZ a unified library for exploratory analysis of Bayesian models in Python |year=2019 |last1=Kumar |first1=Ravin |last2=Carroll |first2=Colin |last3=Hartikainen |first3=Ari |last4=Martin |first4=Osvaldo |journal=Journal of Open Source Software |volume=4 |issue=33 |page=1143 |bibcode=2019JOSS....4.1143K |doi-access=free |hdl=11336/114615 |hdl-access=free }}</ref>

When working with Bayesian models there are a series of related tasks that need to be addressed besides inference itself:

* Diagnoses of the quality of the inference, this is needed when using numerical methods such as [[Markov chain Monte Carlo]] techniques
* Model criticism, including evaluations of both model assumptions and model predictions
* Comparison of models, including model selection or model averaging
* Preparation of the results for a particular audience

All these tasks are part of the Exploratory analysis of Bayesian models approach and successfully performing them is central to the iterative and interactive modeling process. These tasks require both numerical and visual summaries.<ref>{{cite journal |arxiv=1709.01449 |doi=10.1111/rssa.12378 |title=Visualization in Bayesian workflow |year=2019 |last1=Gabry |first1=Jonah |last2=Simpson |first2=Daniel |last3=Vehtari |first3=Aki |last4=Betancourt |first4=Michael |last5=Gelman |first5=Andrew |s2cid=26590874 |journal=Journal of the Royal Statistical Society, Series A (Statistics in Society) |volume=182 |issue=2 |pages=389–402 }}</ref><ref>{{cite journal |arxiv=1903.08008 |last1=Vehtari |first1=Aki |last2=Gelman |first2=Andrew |last3=Simpson |first3=Daniel |last4=Carpenter |first4=Bob |last5=Bürkner |first5=Paul-Christian |title=Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of MCMC (With Discussion) |journal=Bayesian Analysis |year=2021 |volume=16 |issue=2 |page=667 |doi=10.1214/20-BA1221 |bibcode=2021BayAn..16..667V |s2cid=88522683 }}</ref><ref name="Martin2018">{{cite book|url=https://books.google.com/books?id=1Z2BDwAAQBAJ|title=Bayesian Analysis with Python: Introduction to statistical modeling and probabilistic programming using PyMC3 and ArviZ|last1=Martin|first1=Osvaldo|date=2018|publisher=Packt Publishing Ltd|isbn=9781789341652|language=en}}</ref>