**1.**

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.

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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.

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

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

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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.

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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.

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

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

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

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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.

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