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In Bayesian statistics, the term 'posterior' refers to the probability distribution of a parameter conditioned on the observed data.
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Failing to implement Bayesian Chi2 goodness of fit test
The central idea is that the proposed $R^B$ statistic's posterior approaches a $\chi^2_{K-1}$ distribution, where $K$ is the number of discrete values a variable can take. … It is defined as
$$R^B(\tilde\theta) = \sum_{k=1}^K \left[{m_k - n p_k(\tilde\theta) \over \sqrt{np_k(\tilde\theta)}}\right]^2$$
where $\tilde\theta$ is a single posterior draw from the parameter vector …