Bayesian semiparametric inference for statistical models using mixtures

We study mixture models for linear regression, survival analysis, and non-Poisson point processes. The mixture models are used mainly as a device to improve robustness to misspecification of assumptions. The method is semiparametric in the sense that the number of components of the mixture is not fixed but is allowed to depend on the data. We follow a Bayesian approach to inference. Markov chain Monte Carlo is used to sample from the posterior distribution of the parameters and to estimate other quantities of interest. Models can be compared using the Bayesian Information Criterion (BIC). The mixture methods delineated in this thesis have appealing features: they constitute a uniform technique to build models robust to misspecifications; they have broad scope; and they are reasonably well behaved asymptotically. Asymptotic results about the consistency of the posterior distribution are proved. Applications to real data sets include parameter estimation in interval-censored data in survival analysis and estimation of the conditional intensity function of neuronal spike trains. A simulation study to investigate small sample properties is also performed.