Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling

Several new estimators of the marginal likelihood for complex non-Gaussian models are developed. These estimators make use of the output of auxiliary mixture sampling for count data and for binary and multinomial data. One of these estimators is based on combining Chib’s estimator with data augmentation as in auxiliary mixture sampling, while the other estimators are importance sampling and bridge sampling based on constructing an unsupervised importance density from the output of auxiliary mixture sampling. These estimators are applied to a logit regression model, to a Poisson regression model, to a binomial model with random intercept, as well as to state space modeling of count data.