Latent class analysis explains dependency structures in multivariate categorical data by assuming the presence of latent classes. We investigate the specification of suitable priors for the Bayesian latent class model to determine the number of classes and perform variable selection. Estimation is possible using standard tools implementing general purpose Markov chain Monte Carlo sampling techniques such as the software JAGS. However, class specific inference requires suitable post-processing in order to eliminate label switching. The proposed Bayesian specification and analysis method is applied to the Hungarian heart disease data set to determine the number of classes and identify relevant variables and results are compared to those obtained with the standard prior for the component specific parameters.

Shelters often make euthanasia or adoption decisions based on the results of FeLV-FIV point-of-care tests but given the low estimated prevalence of these diseases and imperfect test performance, this might not be a good practice because of diagnostic error. The objectives of this study were to determine the true prevalence of FeLV and FIV in apparently healthy and sick shelter cats in Mississippi, estimate predictive value of the Zoetis Witness FeLV-FIV Rapid ImmunoMigration test results at the estimated true prevalences through Bayesian latent class modeling, and formulate testing recommendations for shelters. One chapter will review the literature on FeLV and FIV. The bulk of this thesis will focus on determining the true prevalence of retroviral infection in Mississippi shelter cat populations. The last chapter will use Bayesian modeling to estimate test performance and predictive value of test results in healthy and sick shelter cat populations.