Grant: Discovery Grants Program - Individual

In this research proposal we consider some aspects of the marginal likelihood as a criterion for Bayesian model selection. The marginal likelihood is defined as the marginal density of the data under a given model, and can be interpreted as a measure of how the data supports the model. The higher this value, the more likely is the model under consideration. Hence, a general rule is to select the model yielding the maximal marginal likelihood value. When we wish to compare two models, the decision can be based on the value of the Bayes factor, which is defined as the ratio of the respective marginal likelihoods. We first want to investigate how to fine-tune some sequential Monte Carlo samplers (SMCS). SMCS are a new class of samplers that can be used for marginal likelihood estimation. We suggest the use of two statistical distances to select sequences of related statistical distributions required for their implementation. Secondly, we will consider possible alternate specifications of the fractional Bayes factor. The fractional Bayes factor is a robust modification of the Bayes factor that is used in the presence of weak prior information on the parameters of the models. We will consider the application of the suggested theoretical developments on Bayesian graphical models applied to biological problems. Finally we will take a new approach on model selection for Marginal Structural Models and consider model averaging. Model averaging consists in taking the weighted mean of a quantity of interest over the models, where the weights are proportional to the marginal likelihood (under the assumption that the models are a priori likely). This should bring an improvement over the usual approach where only one single model is selected for inference.