J. Andrés Christen , Centro de Investigación en Matemáticas, A. C. (CIMAT), Mexico.

joint with Colin Fox, Physics Department, University of Otago, New Zealand.

Title: "A General Purpose Scale-Independent MCMC Algorithm"

Abstract:

We develop a new effectively adaptive, general purpose MCMC for
arbitrary continuous distributions. We call this MCMC the "t-walk". The
t-walk maintains two independent points in the sample space, and
all moves are based on proposals that are then accepted with a
standard Metropolis-Hastings acceptance probability on the product
space. Hence the t-walk may be viewed as an adaptive MCMC sampler
that maintains a set of two points in the state space and moves them
with some structure. However the t-walk is strictly not adaptive on the product space, but does display beneficial self-adjusting behavior on the original state space.
Four proposal distributions, or `moves', are given resulting in an algorithm which is effective in sampling distributions of moderate dimension and arbitrary scale, without
the requirement for further tuning of parameters. Several examples are presented showing very good mixing and convergence characteristics, varying in dimensions
and with radically different scale and correlation structure, using exactly the same sampler.