Simulating sample predictions from test data

Using a test portion of the data that is set aside, this is an algorithm that can be used to simulate sample predictions of the rest of the sample. This can be used to build a distribution of the Bayesian Specification Test.

1. Use Bayes Rule with the training data to get $p(\theta |y_T)$
2. Draw n realizations of $\theta$ from $p(\theta |y_T)$
3. Use these n $\theta$ values to simulate sample data from the likelihood function $p(y|\theta )$ - simulate samples the same size as the rest of the data
4. use the bayesian specification test of the simulated samples - this forms the test distribution
5. Compare to the specification test of the rest of the sample data to see if the model makes sense

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References

@lancaster2004 - Chapter 2