Chapter 11 Exercises
Dirichlet process mixture for eye tracking data
Fit a Dirichlet process mixture of normal distributions to the eye tracking data from Section 11.6.
a) Firstly fit a model with the within-cluster variance of observations restricted to be the same for all clusters, and the Dirichlet process concentration parameter fixed at 1.
b) Then develop a model with different variances in each cluster. For example, use a normal hierarchical prior for the cluster log SD (as suggested in Section 10.4 of the book) with a fixed mean and a mildly informative gamma prior on the precision.
In each case, ensure that the chain for the total number of clusters (and the chains for other parameters) is well-mixing, and plot the posterior distribution of this number.
As in the Galaxy example, include a variable dens.x in the data containing values at which to estimate the density of the mixture distribution. Use Inference -> Compare -> model fit (or some other software) to plot the posterior distribution of this density, and compare to the histogram in Figure 11.6 in the book.