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David Aristoff, Colorado State UniversityDavid Aristoff, Colorado State UniversityEwing 336Title: Piecewise deterministic Markov processes (PDMPs) for efficient sampling <br></br> Abstract: Historically, the Metropolis-Hastings method has been the standard technique for sampling high dimensional probability distributions. However, Metropolis-Hastings methods can have poor performance. One reason is metastability, the tendency for the sampling to become stuck in certain regions. PDMPs can partially overcome this problem by breaking reversibility with momentum-like variables. We give an introduction to PDMPs and discuss applications to simulating many-particle systems.3/12/2018 3:00:00 PM3/12/2018 4:00:00 PMFalse
Dave Caldwell, University of DelawareDave Caldwell, University of DelawareEwing 336TBA12/4/2017 5:00:00 PM12/4/2017 6:00:00 PMFalse
Noah Forman, University of WashingtonNoah Forman, University of WashingtonEwing 336Title: Random walks on a space of trees with integer edge weights <br></br> Abstract: Consider the Markov process in the space of binary trees in which, at each step, you delete a random leaf and then grow a new leaf in a random location on the tree. This is applied in MCMC algorithms for phylogenetic inference. In 2000, Aldous conjectured that it should have a continuum analogue, which would be a continuum random tree-valued diffusion. We will discuss a family of projectively consistent Markov chains that are projections of this tree, and discuss how these representations can be passed to the continuum. This is joint work with Soumik Pal, Douglas Rizzolo, and Matthias Winkel. 11/27/2017 8:30:00 PM11/27/2017 9:30:00 PMFalse
Steve Melczer, University of PennsylvaniaSteve Melczer, University of PennsylvaniaEwing 336TITLE: Lattice Path Enumeration, Multivariate Singularity Analysis, and Probability Theory <br><br> ABSTRACT: The problem of enumerating lattice paths with a fixed set of allowable steps and restricted endpoint has a long history dating back at least to the 19th century. For several reasons, much research on this topic over the last decade has focused on two dimensional lattice walks restricted to the first quadrant, whose allowable steps are "small" (that is, each step has coordinates +/- 1, or 0). In this talk we relax some of these conditions and discuss recent work on walks in higher dimensions, with non-small steps, or with weighted steps. Particular attention will be given to the asymptotic enumeration of such walks using representations of the generating functions as diagonals of rational functions, through the theory of analytic combinatorics in several variables. Several techniques from computational and experimental mathematics will be highlighted, and open conjectures of a probabilistic nature will be discussed. 11/6/2017 8:30:00 PM11/6/2017 9:30:00 PMFalse

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