10 Facts About Bayesian statistics

Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event.

Bayesian statistics is named after Thomas Bayes, who formulated a specific case of Bayes' theorem in a paper published in 1763.

Many Bayesian statistics methods were developed by later authors, but the term was not commonly used to describe such methods until the 1950s.

Many Bayesian statistics methods required much computation to complete, and most methods that were widely used during the century were based on the frequentist interpretation.

However, with the advent of powerful computers and new algorithms like Markov chain Monte Carlo, Bayesian methods have seen increasing use within statistics in the 21st century.

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Maximum a posteriori, which is the mode of the posterior and is often computed in Bayesian statistics using mathematical optimization methods, remains the same.

Bayesian statistics inference refers to statistical inference where uncertainty in inferences is quantified using probability.

Bayesian statistics inference uses Bayes' theorem to update probabilities after more evidence is obtained or known.

Formulation of statistical models using Bayesian statistics has the identifying feature of requiring the specification of prior distributions for any unknown parameters.

Exploratory analysis of Bayesian statistics models is an adaptation or extension of the exploratory data analysis approach to the needs and peculiarities of Bayesian statistics modeling.