Bayesian statistical methodology is based on Bayes' Theorem:

- .

- P(
*A*) is the prior probability of*A*. It is "prior" in the sense that it does not take into account any information about*B*. - P(
*A*|*B*) is the conditional probability of*A*, given*B*. It is also called the posterior probability because it is derived from or depends upon the specified value of*B*. - P(
*B*|*A*) is the conditional probability of*B*given*A*. - P(
*B*) is the prior or marginal probability of*B*. - Generally, in Bayesian inference,
*A*represents the model, while*B*represents the data.

There are two common schools of thought on Bayesian inference, the *objectivist* view and the *subjectivist* view. Objectivists view probability statements as an extension of logic. Subjectivists view them as measures of "personal belief."

## External LinksEdit

## Bayes Recommendations From The ChannelEdit

< gzl> http://www.uv.es/bernardo/BayesStat.pdf

< papshmear> box/tiao, http://www.amazon.com/Bayesian-Inference-Statistical-Analysis-Classics/dp/0471574287 is okay for the mathematical background

<papshmear> http://bayes.wustl.edu/gregory/articles.pdf

< papshmear> An Introduction to Bayesian Inference and Decision by Winkler, http://www.amazon.com/Introduction-Bayesian-Inference-Decision-Second/dp/0964793849 is quite nice

< papshmear> Gregories, http://www.amazon.com/Bayesian-Logical-Analysis-Physical-Sciences/dp/052184150X, is okay but he's a maxent fanboy too

< sevenless> DS Sivia's book: http://www.amazon.com/Data-Analysis-Bayesian-Tutorial-Publications/dp/0198518897

< sevenless> Gelman 2003, Bayesian Data Analysis, http://www.stat.columbia.edu/~gelman/book/ is nice after Sivia

< sevenless> Gelman and Hill, 2007, on applied multilevel modeling and causal inference, http://www.stat.columbia.edu/~gelman/arm/