Bayesian Specification Test

Used to test if the data fits the Predictive distribution of the model.

Its a scalar function that preferably takes into account model assumptions of the data (for example, do residuals need to be normally distributed).

Can be used to make test distribution for the predictive distribution . Then a test statistic can be used on the sample data to infer if the sample data is probable given the specification test distribution. Can steal frequentist test statistics for this (if they make sense).

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References

@lancaster2004 - Chapter 2