Fuelled by the proliferation of large and complex data sets, statistical modelling has become increasingly ambitious. In fact, the use of models parameterised by an infinite number of parameters or latent variables is increasingly common. This is particularly appealing when models are most naturally formulated within an infinite dimensional setting, for instance continuous time-series.
It is well-understood that to obtain widely applicable statistical methodology for flexible families of complex models, requires powerful computational techniques (such as MCMC, SMC, etc). Unfortunately, infinite dimensional simulation is not usually feasible, so that the use of these computational methods for infinite-dimensional models is often only possible by adopting some kind of finite dimensional approximation to the chosen model. This is unappealing since the impact of the approximation is often difficult to assess, and the procedure often involves essentially using an approximate finite-dimensional model.
The talk will discuss a general technique for simulation which attempts to work directly with infinite dimensional random variables without truncation nor approximation. The talk is illustrated by concrete examples from the simulation of diffusion processes and Bayesian inference for Dirichlet mixture models. One surprising feature of the methodology is that exact infinite-dimensional algorithms are commonly far more efficient than approximate models