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.
We investigated an approach the sampling problem that breakins the probability distribution to be sampled into smaller pieces that correspond to the most important regions, and piecing the results together. This technique is called stratification, and the smaller pieces are called the ‘strata’.
We developed a rigorous theory of this class of stratified sampling methods, which explains the way they break down complex distributions in terms of probability theory. We used this to determine conditions under which they converge to the correct distribution over time, which was a novel and useful result.