In the Gibbs sampling algorithm, we start by reducing all the factors with the observed variables. After this, we generate a sample for each unobserved variable on the prior using some sampling method, for example, by using a mutilated Bayesian network. After generating the first sample, we iterate over each of the unobserved variables to generate a new value for a variable, given our current sample for all the other variables.

Let's take the example of our restaurant model to make this clearer. Assume that we have already observed that the cost of the restaurant is high. So, we will have the CPDs: . We start by generating our first sample with forward sampling, and let's say our first samples are and . We will now iterate over all of our unobserved variables N, L, Q. Starting with N, we will sample it from the distribution . As we are computing the distribution over a single variable, we can compute it very easily as follows:

Now that we have sampled from the distribution...