A0364
Title: Importance tempering of Markov chain Monte Carlo methods
Authors: Quan Zhou - Texas A&M University (United States) [presenting]
Aaron Smith - University of Ottawa (Canada)
Guanxun Li - Texas A&M University (United States)
Abstract: Informed importance tempering (IIT) is an easy-to-implement MCMC algorithm that can be seen as an extension of the familiar Metropolis-Hastings algorithm with the special feature that informed proposals are always accepted and which was shown to converge much more quickly in some common circumstances. A new, comprehensive guide is developed for the use of IIT in many situations. First, two IIT schemes are proposed that run faster than existing informed MCMC methods on discrete spaces by not requiring the posterior evaluation of all neighbouring states. Second, IIT is integrated with other MCMC techniques, including simulated tempering, pseudo-marginal and multiple-try methods (on general state spaces), which have been conventionally implemented as Metropolis-Hastings schemes and can suffer from low acceptance rates. The use of IIT allows to always accept proposals and brings about new opportunities for optimizing the sampler, which is not possible under the Metropolis-Hastings framework. Numerical examples illustrating the findings are provided for each proposed algorithm, and a general theory on the complexity of IIT methods is developed.
