| Abstract: |
| In this talk we will consider how transport maps can simplify the problem of sampling from complex posterior distributions using adaptive importance sampling methods. Adaptive importance sampling or population Monte Carlo methods use a mixture distribution to approximate the posterior, in order to produce an efficient importance sampling scheme. However if there are complex structures such as strong correlations or sharp ridges in the posterior, these methods require a large increase in the number of ensemble members, or they may become unstable. In this work, we investigate the use of transport maps to stabilise and speed up sampling using these methods for such problems with no increase in the size of ensemble. The transport map is chosen, following work by Marzouk and Parno, through the sample obtained so far from the posterior, to minimise the KL divergence between the push-forward of the posterior through the map, and a reference Gaussian. This simplifies greatly the problem of sampling from such a distribution. We will demonstrate the approach through some numerical examples. |
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