Next generation adaptive Markov chain Monte Carlo algorithms

Project ID: 2531ad1583

(You will need this ID for your application)

UCL Lead department: Statistical Science

Project Summary:

Why this research is important? Adaptive Markov chain Monte Carlo (MCMC) is a very effective approach to sampling from complex probability distributions that arise in Bayesian statistics as well as statistical physics, inverse problems, machine learning and many other areas. The current suite of adaptive MCMC algorithms do, however, struggle to sample efficiently from distributions that are far from elliptical in shape or of high dimension, in the latter case due to the large computational cost of adaptation. In this project we will design new adaptive MCMC algorithms that are carefully tailored to these settings.

Who will you be working with? Dr Samuel Livingstone, associate professor in Statistical Science and expert in Markov chain Monte Carlo algorithms.

What will you be doing? In the first instance we will seek to exploit recent work on skew-symmetric posterior approximations to design light-weight nonlinear adaptive MCMC algorithms. We will also use factor models and other low-dimensional encoder approaches to design computationally cheap high-dimensional adaptive algorithms. In addition we will explore the extent to which Hamiltonian dynamics, which are a natural output of the popular Hamiltonian Monte Carlo algorithm, can be used to speed up adaptive MCMC algorithms.

Who we are looking for? The project will contain some mathematical work on designing Markov processes and studying convergence to equilibrium, and programming skills in testing out methods empirically, and will therefore suit a student who is interested in both of these areas. You will have a strong background in both mathematics and scientific programming in either R, python, Julia or a related language. Some familiarity with MCMC algorithms is desirable.