Bayesian prediction algorithm

1. Use Bayes rule to get posterior distribution $p(\theta |y^{obs})$ - can use sampling algorithm to approximate the distribution
2. Sample $\theta$ from posterior
3. Use sampled $\theta$‘s (and $y^{obs}$ if you need to) to draw realizations from the distribution function $f_{\tilde{Y}|y^{obs},\theta }$ - this is the ‘new’ likelihood function.

These draws from this algorithm are from the Posterior Predictive Distribution

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References

@lancaster2004 - Chapter 2