Posterior Predictive Distribution

Given the model and the data, what would we expect another realization of the data to look like (statistically)?

$p(\tilde{y}|y^{obs})={\int }_{\theta }p(\tilde{y}|y^{obs},\theta )p(\theta |y^{obs})d\theta$

Is similar to the Predictive distribution, but it has the extra conditioning factor $y^{obs}$

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References

@lancaster2004 - Chapter 2 Bayesian prediction algorithm - can use this to simulate a lot of realizations and approximate the distribution