Abstract This talk will introduce three new tools for summarizing a probability distribution more effectively than independent sampling or standard Markov chain Monte Carlo thinning: 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. If the initial summary suffers from biases due to off-target sampling, tempering, or burn-in, Stein thinning simultaneously compresses the…