This talk will introduce two new tools for summarizing a probability distribution more effectively than independent sampling or standard Markov chain Monte Carlo thinning:

1. Given an initial n point summary (for example, from independent sampling or a Markov chain), kernel thinning finds a subset of only square-root n points with comparable worst-case integration error across a reproducing kernel Hilbert space.
2. If the initial summary suffers from biases due to off-target sampling, tempering, or burn-in, Stein thinning simultaneously compresses the summary and improves the accuracy by correcting for these biases.

These tools are especially well-suited for tasks that incur substantial downstream computation costs per summary point like organ and tissue modeling in which each simulation consumes 1000s of CPU hours.