Ola Jonasson presenterar sitt examensarbete


Efficiency in Reversible Jump MCMC for Mixture Models regarding Latent Variables

Abstract

A mixture model is a statistical model where a sample is considered to
be drawn from one component, where every component has different
properties. With the Reversible Jump MCMC method, inference can be
made on mixture models with an unknown number of components. In the
Metropolis-Hastings move of the algorithm the likelihood function of
the mixture model is to be calculated, and here is a choice to include
or exclude so called latent variables. These latent variables act as
labels and describe from what component a given sample is taken from.

Two cases were studied in this thesis. In the first, with a moderate
number of observations, the efficiency of the reversible jump MCMC
algorithm without latent variables was higher both for the number of
components and for the component-wise means. In the second, with a
considerable amount of observations, the acceptance rate for the
Metropolis-Hastings move was very low for the algorithm with latent
variables. The conclusion is a recommendation to use the algorithm
without latent variables in the likelihood.