10.6 Diagnosing the samples

In this book, we have used numerical methods to compute the posterior for virtually all models. That will most likely be the case for you, too, when using Bayesian methods for your own problems. Since we are approximating the posterior with a finite number of samples, it is important to check whether we have a valid sample; otherwise, any analysis from it will be totally flawed. There are several tests we can perform, some of which are visual and others quantitative. These tests are designed to spot problems with our samples, but they are unable to prove we have the correct distribution; they can only provide evidence that the sample seems reasonable. If we find problems with the sample, there are many solutions to try. We will discuss them along with the diagnostics.

To make the explanations concrete, we are going to use minimalist models, with two parameters: a global parameter a and a group parameter b. And that’s it, we do not even have likelihood...