Predictive distribution

Is the probability of what the data should look like (theoretically and independent of it being sampled)

Is based off the prior distribution.

$p(y)={\int }_{\theta }p(y|\theta )p(\theta )d\theta$ A lot of times it’s easier to sample this a bunch of times to get the distribution instead of trying to do the integration analytically.

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References

@lancaster2004 - chapter 2