## Sequential Importance Sampling; Three Examples and a Theorem

### Persi Diaconis / Stanford University

Bio: Persi Diaconis is Professor of Mathematics and Statistics at Stanford University. He works in probability, combinatorics, mathematical statistics and group theory. Perhaps most well known for proving that 'Seven ordinary riffle shuffles are necessary and suffice to mix up 52 cards'. This is a typical result in a main interest; proving rates of convergence to equilibrium for widely used Markov Chain Monte Carlo algorithms. In combinatorics he works on the enumerative, probabilistic side; pick and x in X at random, what does it look like? This often leans on tools like symmetric function theory. In Mathematical statistics, he proves (and disproves) things about Bayesian procedures; the standard notion of conjugate prior and the inconsistency of Bayes procedures in non-parametric problems. In Group theory he has developed new 'supercharacter theories' for provably intractable cases and the 7/9 theorem; if S is a subset of the finite group G and the chance that the product of a pair of random elements of S is in S is larger than 7/9 then S is a subgroup. For most of his career he has been fascinated by the interface between 'the art of computer programming' and his areas of expertise.