Abstract

Let (X_t, t\ge 0) be defined as a solution to a stochastic (partial) differential equation. Suppose X is partially observed at n fixed time instances and that its dynamics are parametrised by a finite-dimensional parameter theta.  I will consider recent work on sampling latent paths of the process and the parameter, conditional on the data. The key idea behind the approach is to consider a change of measure on path space that turns the forward process into the conditioned process. By approximating this change of measure we can obtain weighted samples from the conditioned process. Making this idea precise turns out to be much more involved for SPD Es compared to the SDE case. Some numerical results will show strengths and limitations of the methods proposed. Joint work with Thorben Pieper-Sethmacher, Moritz Schauer and Aad van der Vaart.