We present an approach to Bayesian model selection for finitely observed diffusion processes. We use data augmentation by treating the paths between observed points as missing data. For a fixed model formulation, the strong dependence between the missing paths and the volatility of the diffusion...

We consider estimation of scalar functions that determine the dynamics of diffusion processes. It has been recently shown that nonparametric maximum likelihood estimation is ill-posed in this context. We adopt a probabilistic approach to regularize the problem by the adoption of a prior...

Inference for Dirichlet process hierarchical models is typically performed using Markov chain Monte Carlo methods, which can be roughly categorized into marginal and conditional methods. The former integrate out analytically the infinite-dimensional component of the hierarchical model and sample...