In this research project my co-author and I explored the problem of sampling from complex probability distributions with multiple high-probability regions that are hard to find. Generating such samples has many applications in, for example, molecular dynamics, where the sampless correspond to different chemical states of a system.
Here we analyzed an algorithm that alternated between sampling from smaller parts of the target distribution, called ‘strata’, and patching the results together to form samples from the whole distribution. This technique can overcome the problem of distributions with multiple important regions that are hard to connect, a common scenario in molecular dynamics.
We made major strides in understanding how such an algorithm performs under given conditions. We derived precise bounds on the algorithm’s speed of convergence towards the distribution it estimates. Furthermore, we expressed the performance in terms of a concrete metric for how well the strata are chosen, making my results useful in practice.