Abstract
We aim to improve upon the exploration of the general-purpose random walk Metropolis algorithm when the target has non-convex support Asubset {mathbb {R}}^d, by reusing proposals in A^c which would otherwise be rejected. The algorithm is Metropolis-class and under standard conditions the chain satisfies a strong law of large numbers and central limit theorem. Theoretical and numerical evidence of improved performance relative to random walk Metropolis are provided. Issues of implementation are discussed and numerical examples, including applications to global optimisation and rare event sampling, are presented.
Highlights
A key challenge for Markov chain Monte Carlo (MCMC) algorithms is the balance between global “exploration” and local “exploitation”
In this paper we present the skipping sampler, a general-purpose and implemented Metropolis-class algorithm which is capable of improving exploration of targets π with nontrivial support A, by reusing proposals lying outside A
The resulting Markov chain satisfies a strong law of large numbers and central limit theorem under essentially the same conditions as for random walk Metropolis (RWM), to which we provide theoretical and numerical performance comparisons
Summary
A key challenge for Markov chain Monte Carlo (MCMC) algorithms is the balance between global “exploration” and local “exploitation”. In this paper we present the skipping sampler, a general-purpose and implemented Metropolis-class algorithm which is capable of improving exploration of targets π with nontrivial support A, by reusing proposals lying outside A For this to be useful, we make the following standing assumption: Assumption 1 π is a probability density function on Rd whose support. To accelerate global exploration of the state space in MCMC algorithms, several approaches have been developed including tempering, Hamiltonian Monte Carlo and piecewise deterministic methods (see Robert et al (2018) for a recent review) These methods are best suited to target densities with connected support, since the chain cannot cross regions where the target has zero density. A disconnected support would imply reducibility of the chain and its failure to converge to the target
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
