What is Bayesian statistics?

Bayesian statistics is a theory in the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief known as Bayesian probabilities. Such an interpretation is only one of a number of interpretations of probability and there are other statistical techniques that are not based on ‘degrees of belief’. One of the key ideas of Bayesian statistics is that “probability is orderly opinion, and that inference from data is nothing other than the revision of such opinion in the light of relevant new information. The formulation of statistical models using Bayesian statistics has the unique feature of requiring the specification of prior distributions for any unknown parameters. These prior distributions are as integral to a Bayesian approach to statistical modeling as the expression of probability distributions. The Bayesian design of experiments includes a concept called ‘influence of prior beliefs’. This approach uses sequential analysis techniques to include the outcome of earlier experiments in the design of the next experiment. This is achieved by updating ‘beliefs’ through the use of prior and posterior distribution. This allows the design of experiments to make good use of resources of all types.

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