In the case of full particles for importance sampling, we used to generate particles from another distribution, and then, to compensate for the difference, we used to associate a weighting to each particle. Similarly, in the case of collapsed particles, we will be generating particles for the variables and getting the following dataset:

Here, the sample is generated from the distribution Q. Now, using this set of particles, we want to find the expectation of relative to the distribution :

Fig 4.22: The late-for-school model

Let's take an example using the late-for-school model, as shown in Fig 4.22. Let's consider that we have the evidence that , , and partition the variables as and . So, we will generate particles over the variable . Also, each such particle is associated with the distribution . Now, assuming some query (say ), our indicator function will be . We will now evaluate for each particle:

After this, we will compute the average of these probabilities...