Editing Bayesian inference (section)

==Further reading==

* For a full report on the history of Bayesian statistics and the debates with frequentists approaches, read {{cite book |last=Vallverdu |first=Jordi |title=Bayesians Versus Frequentists A Philosophical Debate on Statistical Reasoning |publisher=Springer |year=2016 |location=New York |isbn=978-3-662-48638-2 }}
* {{Cite book |last=Clayton |first=Aubrey |author-link=Aubrey Clayton|url=https://cup.columbia.edu/book/bernoullis-fallacy/9780231199940 |title=Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science |date=August 2021 |publisher=Columbia University Press |isbn=978-0-231-55335-3}}

===Elementary===
The following books are listed in ascending order of probabilistic sophistication:
* Stone, JV (2013), "Bayes' Rule: A Tutorial Introduction to Bayesian Analysis",   [http://jim-stone.staff.shef.ac.uk/BookBayes2012/BayesRuleBookMain.html Download first  chapter here], Sebtel Press, England.
* {{Cite book| title=Understanding Uncertainty, Revised Edition| author=Dennis V. Lindley | publisher=John Wiley | year=2013| edition=2nd | isbn=978-1-118-65012-7| author-link=Dennis V. Lindley }}
* {{Cite book| title=Scientific Reasoning: The Bayesian Approach| author=Colin Howson |author2=Peter Urbach |name-list-style=amp | publisher=[[Open Court Publishing Company]]| year=2005| edition=3rd | isbn=978-0-8126-9578-6| author-link=Colin Howson }}
* {{Cite book|author=Berry, Donald A.|title=Statistics: A Bayesian Perspective|publisher=Duxbury| year=1996|isbn=978-0-534-23476-8}}
*{{Cite book|author=Morris H. DeGroot|author2=Mark J. Schervish|name-list-style=amp|title=Probability and Statistics|edition=third|isbn=978-0-201-52488-8|publisher=Addison-Wesley|year=2002|url-access=registration|url=https://archive.org/details/probabilitystati00degr_0|author-link=Morris H. DeGroot}}
* Bolstad, William M. (2007) ''Introduction to Bayesian Statistics'': Second Edition, John Wiley {{ISBN|0-471-27020-2}}
*{{cite book |author=Winkler, Robert L |title=Introduction to Bayesian Inference and Decision |publisher=Probabilistic |year=2003 |isbn=978-0-9647938-4-2 |edition=2nd  }} Updated classic textbook. Bayesian theory clearly presented.
* Lee, Peter M. ''Bayesian Statistics: An Introduction''. Fourth Edition (2012), John Wiley {{ISBN|978-1-1183-3257-3}}
* {{Cite book| title = Bayesian Methods for Data Analysis, Third Edition | publisher = Boca Raton, FL: Chapman and Hall/CRC | year = 2008 | isbn = 978-1-58488-697-6|author1=Carlin, Bradley P.  |author2=Louis, Thomas A. |name-list-style=amp }}
* {{Cite book| title = Bayesian Data Analysis, Third Edition | publisher = Chapman and Hall/CRC | year = 2013 | isbn = 978-1-4398-4095-5|last1=Gelman|first1=Andrew|author-link1=Andrew Gelman|last2=Carlin|first2=John B.|last3=Stern|first3=Hal S.|last4=Dunson|first4=David B.|last5=Vehtari|first5=Aki|last6=Rubin|first6=Donald B.|author-link6=Donald Rubin}}

===Intermediate or advanced===
* {{Cite book|author=Berger, James O| title=Statistical Decision Theory and Bayesian Analysis| edition=Second|year=1985| publisher=Springer-Verlag|series=Springer Series in Statistics|isbn=978-0-387-96098-2| bibcode=1985sdtb.book.....B| author-link=James Berger (statistician)}}
*{{Cite book|title=Bayesian Theory|publisher=Wiley|year=1994|author-link1=José-Miguel Bernardo|last1=Bernardo|first1=José&nbsp;M.|author-link2=Adrian Smith (statistician)|last2=Smith|first2=Adrian&nbsp;F.&nbsp;M.}}
* [[Morris H. DeGroot|DeGroot, Morris H.]], ''Optimal Statistical Decisions''. Wiley Classics Library. 2004. (Originally published (1970) by McGraw-Hill.) {{ISBN|0-471-68029-X}}.
* {{cite book|title=Theory of statistics|first=Mark J.|last=Schervish|publisher=Springer-Verlag|year=1995|isbn=978-0-387-94546-0}}
* Jaynes, E. T. (1998). [http://www-biba.inrialpes.fr/Jaynes/prob.html ''Probability Theory: The Logic of Science''].
* O'Hagan, A. and Forster, J. (2003). ''Kendall's Advanced Theory of Statistics'', Volume 2B: ''Bayesian Inference''. Arnold, New York. {{ISBN|0-340-52922-9}}.
* {{Cite book|author=Robert, Christian P|title=The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation|publisher=Springer|year=2007|edition=paperback|isbn=978-0-387-71598-8}}
* [[Judea Pearl|Pearl, Judea]]. (1988). ''Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference'', San Mateo, CA: Morgan Kaufmann.
* Pierre Bessière et al. (2013). "[http://www.crcpress.com/product/isbn/9781439880326 Bayesian Programming]". CRC Press. {{ISBN|9781439880326}}
* Francisco J. Samaniego (2010). "A Comparison of the Bayesian and Frequentist Approaches to Estimation". Springer. New York, {{ISBN|978-1-4419-5940-9}}