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

Indeed, parameters of prior distributions may themselves have prior distributions, leading to Bayesian hierarchical modeling, or may be interrelated, leading to Bayesian networks.

It is therefore desirable to make a few statements about these procedures that be conveniently under the general term of statistical modelling.

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Laplace used methods that would now be considered as Bayesian methods to solve a number of statistical problems.

Probabilities are not assigned to parameters or hypotheses in frequentist inference.

For example, it would not make sense in frequentist inference to directly assign a probability to an event that can only happen once, such as the result of the next flip of a fair coin.

Many Bayesian methods required a lot of 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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