In Bayesian analysis, the posterior distribution, or posterior, is the distribution of a set of unknown parameters, latent variables, or otherwise missing variables of interest, conditional on the current data. The posterior distribution uses the current data to update previous knowledge, called a prior, about that parameter. A posterior distribution, p(θ|x), is derived using Bayes’s theorem
where θ is the unknown parameter(s) and x is the current data. The probability of the data given the parameter p(x|θ) is the likelihood L(θ|x). The prior distribution, p(θ), is user specified to represent prior knowledge about the unknown parameter(s). The last piece of Bayes’s theorem, the marginal [Page 1274]distribution of data, p(x), is computed using the likelihood and the prior. The distribution of the posterior is determined by the ...
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