The Importance Markov Chain

07/17/2022
by   Charly Andral, et al.
0

The Importance Markov chain is a new algorithm bridging the gap between rejection sampling and importance sampling, moving from one to the other using a tuning parameter. Based on a modified sample of an auxiliary Markov chain targeting an auxiliary target (typically with a MCMC kernel), the Importance Markov chain amounts to construct an extended Markov chain where the marginal distribution of the first component converges to the target distribution. We obtain the geometric ergodicity of this extended kernel, under mild assumptions on the auxiliary kernel. As a typical example, the auxiliary target can be chosen as a tempered version of the target, and the algorithm then allows to explore more easily multimodal distributions. A Law of Large Numbers and a Central limit theorem are also obtained. Computationally, the algorithm is easy to implement and can use preexisting librairies to simulate the auxiliary chain.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/16/2022

Score-Based Diffusion meets Annealed Importance Sampling

More than twenty years after its introduction, Annealed Importance Sampl...
research
07/19/2013

Kernel Adaptive Metropolis-Hastings

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the p...
research
05/18/2018

Markov Chain Importance Sampling - a highly efficient estimator for MCMC

Markov chain algorithms are ubiquitous in machine learning and statistic...
research
01/25/2020

The reproducing Stein kernel approach for post-hoc corrected sampling

Stein importance sampling is a widely applicable technique based on kern...
research
11/17/2015

Accelerating pseudo-marginal Metropolis-Hastings by correlating auxiliary variables

Pseudo-marginal Metropolis-Hastings (pmMH) is a powerful method for Baye...
research
06/08/2020

Random derangements and the Ewens Sampling Formula

We study derangements of {1,2,...,n} under the Ewens distribution with p...
research
10/28/2022

BRATsynthetic: Text De-identification using a Markov Chain Replacement Strategy for Surrogate Personal Identifying Information

Objective: Implement and assess personal health identifying information ...

Please sign up or login with your details

Forgot password? Click here to reset