Archive for March, 2011
Next Tuesday at 12:15 I’ll be giving the talk in the Algebra, Number Theory, and Combinatorics Seminar in Claremont. The subject is my shiny new protocol for Perfect Simulation: Partially Recursive Acceptance/Rejection in Millikan 208 at Pomona College. Here’s the abstract:
Abstract. Many combinatorial structures can be viewed as colorings of a graph. These structures tend to be self-reducible: once you fix the color of a particular node, the remaining problem is a version of the original on a smaller graph. For instance, independent sets of a graph can be viewed as a coloring where nodes are given color 0 or 1, and no two nodes colored 1 are adjacent to one another. The hard core gas model assigns a probability to each independent set proportional to a parameter lambda raised to the number of 1’s in the graph. In this talk I will introduce a new protocol for designing algorithms to generate random variates drawn from this type of distribution. Called “partially recursive acceptance/rejection”, or PRAR, this protocol can draw samples from self-reducible problems in polynomial time over a restricted set of parameters.
This past Tuesday I gave a talk in the Natural Sciences Seminar Series at Pepperdine. The talk (which has now been posted on my Research talk web page here) is another in the series about TPA.
Abstract. Monte Carlo methods use random variates in order to approximate high dimensional integrals. The resulting estimates have a variance that can vary widely from problem to problem. If constructed poorly the resulting variance can even be infinite. In this talk I will present a new method for estimating integrals where the tightness of the estimate is a direct function of the number of samples. In other words, there is no need to worry about the variance of the estimate, it can be set to any level of precision that the user desires. The method operates by drawing random variates from a sequence of distributions that is determined adaptively at the running time of the algorithm.
The proceedings of the 9th Valencia International Meeting on Bayesian Statistics is now complete, and will be printed by Oxford University Press. This is Sarah’s first publication of her dissertation research, so congratulations to her!
Huber, M. and Schott, S., Using TPA for Bayesian Inference (with discussion), Bayesian Statistics 9, pp. 257–282, 2011.