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Informed MCMC methods have been proposed as scalable solutions to Bayesian posterior computation on high-dimensional discrete state spaces. We study a class of MCMC schemes called informed importance tempering (IIT), which combine importance sampling and informed local proposals. Spectral gap bounds for IIT estimators are obtained, which demonstrate the remarkable scalability of IIT samplers for unimodal target distributions. The theoretical insights acquired in this note provide guidance on the choice of informed proposals in model selection and the use of importance sampling in MCMC methods.
Parallel tempering (PT) is a class of Markov chain Monte Carlo algorithms that constructs a path of distributions annealing between a tractable reference and an intractable target, and then interchanges states along the path to improve mixing in the
Among Monte Carlo techniques, the importance sampling requires fine tuning of a proposal distribution, which is now fluently resolved through iterative schemes. The Adaptive Multiple Importance Sampling (AMIS) of Cornuet et al. (2012) provides a sign
Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of $N$ interacting auxiliary chains targeting temper
The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation $widehat{ESS}$ of the theoretical ESS de
The likelihood-informed subspace (LIS) method offers a viable route to reducing the dimensionality of high-dimensional probability distributions arisen in Bayesian inference. LIS identifies an intrinsic low-dimensional linear subspace where the targe