On the accept-reject mechanism for Metropolis-Hastings algorithms. (English) Zbl 1533.65022
The main contribution of this work is the presentation of a fairly general method to define reversible Markov chains with respect to a given target measure, from a given proposal kernel on an extended state space, by defining a suitable acceptance probability. This extends the classical Metropolis-Hastings settings, and more precisely it is shown to be equivalent to the general settings of a work of Tierney in 1998. By contrast to the latter, the present method is written in a way which is reminiscent of the Hamiltonian Monte Carlo algorithm, which may be easier to interpret and thus to apply. The method is meant to be very versatile, covering in particular infinite-dimensional problems or non-separable Hamilonian schemes. Half of the work is concerned with examples, unifying many popular samplers and introducing some variations, motivated in particular by the use of so-called “surrogate dynamics” which can be used in place of the standard Hamiltonian dynamics with a reduce numerical cost.
Reviewer: Pierre Monmarché (Paris)
MSC:
| 65C40 | Numerical analysis or methods applied to Markov chains |
| 60J22 | Computational methods in Markov chains |
| 65C05 | Monte Carlo methods |
Keywords:
Markov chain Monte Carlo (MCMC) algorithms; Metropolis-Hastings algorithms, sampling on abstract state spaces; Hamiltonian Monte Carlo; surrogate trajectory methodsReferences:
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