Statistics Seminars: A General Construction for Parallelising Metropolis-Hastings Algorithms
8 December 2014 14:00 in CM221
Markov chain Monte Carlo methods are essential tools for solving many
modern day statistical and computational problems, however a major
limitation is the inherently sequential nature of these algorithms. In
this talk I'll present some work I recently published in PNAS on a natural
generalisation of the Metropolis-Hastings algorithm that allows for
parallelising a single chain using existing MCMC methods. We can do so by
proposing multiple points in parallel, then constructing and sampling from
a finite state Markov chain on the proposed points such that the overall
procedure has the correct target density as its stationary distribution.
The approach is generally applicable and straightforward to implement.
I'll demonstrate how this construction may be used to greatly increase the
computational speed and statistical efficiency of a variety of existing
MCMC methods, including Metropolis-Adjusted Langevin Algorithms and
Adaptive MCMC. Furthermore, I'll discuss how it allows for a principled
way of utilising every integration step within Hamiltonian Monte Carlo
methods; our approach increases robustness to the choice of algorithmic
parameters and results in increased accuracy of Monte Carlo estimates with
little extra computational cost.
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