Markov Chain Monte Carlo Estimation
In a Bayesian analysis, the posterior distribution is the solution obtained from fitting the model to the data. Analytical solutions are available for simple models with conjugate priors, such as the beta-binomial model, or a model for the mean of a normal distribution with a known variance. These situations arise when the likelihood is a member of the general exponential family of distributions (Bernardo & Smith, 2000), so that a special related distribution exists that can be used as a prior, and the posterior takes the same form with updated parameters.
Many complex statistical and psychometric models do not enjoy the benefit of having conjugate priors. When there is no closed form solution for the ...
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