Abstract

We propose a method for approximating integrated likelihoods in finite mixture models. We formulate the model in terms of the unobserved group memberships, z, and make them the variables of integration. The integral is then evaluated using importance sampling over the z. We propose an adaptive importance sampling function which is itself a mixture, with two types of component distributions, one concentrated and one diffuse. The more concentrated type of component serves the usual purpose of an importance sampling function, sampling mostly group assignments of high posterior probability. The less concentrated type of component allows for the importance sampling function to explore the space in a controlled way to find other, unvisited assignments with high posterior probability. Components are added adaptively, one at a time, to cover areas of high posterior probability not well covered by the current important sampling function. The method is called Incremental Mixture Importance Sampling (IMIS). IMIS is easy to implement and to monitor for convergence. It scales easily for higher dimensional

Citations