Simulating distribution
Often times it’s much easier to just simulate/ sample from a distribution rather than try to find an analytical solution. Sometimes the integrations needed to marginalize a distribution are impossible. Instead, just generate n realizations from the distribution, and fit a smooth(ish) curve to the histogram. This can ensure an arbitrary level of accuracy since you can decide the number of draws that you want to generate from the distribution.
References
- @lancaster2004 - This is a general theme of the book. Especially chapter 5
- Posterior Predictive Distribution
- Simulating sample predictions from test data
- Bayesian prediction algorithm