| Summary: | Computing posterior distributions over variables linked by deterministic constraints is a recurrent problem in Bayesian analysis. Such problems can arise due to censoring, identifiability issues, or other considerations. It is well-known that standard implementations of Monte Carlo inference strategies break down in the presence of these deterministic relationships. Although several alternative Monte Carlo approaches have been recently developed, few are applicable to deterministic relationships on continuous random variables. In this thesis, I propose Deterministic relationship Sequential Monte Carlo (DrSMC), a new Monte Carlo method for continuous variables possessing deterministic constraints. My exposition focuses on developing a DrSMC algorithm for computing the posterior distribution of a continuous random vector given its sum. I derive optimal settings for this algorithm and compare its performance to that of alternative approaches in the literature. === Science, Faculty of === Statistics, Department of === Graduate
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