| Introduced in 2004, Population Monte Carlo (PMC) is a population-based method that is essentially iterated importance sampling with sample-dependent proposals. The PMC method adapts the proposal distribution to the target distribution by resampling the proposals according to their importance weights and building proposal kernels around the resampled points. The construction of PMC estimator is similar to importance sampling, hence it avoids the difficulties one will come across in justifying the adaptivity of an adaptive MCMC sampler and consistency of the resulting MCMC estimator, where Markovity needs to be preserved. This thesis proposes a new PMC method that weighs the proposals in a different way than the original PMC method by using data reinforcement, derives its theoretical properties, and shows its superiority over the original PMC method in settings where the target distribution is multi-modal or is concentrated around a lower dimensional manifold. It also considers the computational issues in comparing the PMC methods and shows how the new PMC method can be applied to missing data problems. |
