Related papers: Weak Poincar\'e inequality comparisons for ideal a…
It is known that the simple slice sampler has robust convergence properties, however the class of problems where it can be implemented is limited. In contrast, we consider hybrid slice samplers which are easily implementable and where…
Different Markov chains can be used for approximate sampling of a distribution given by an unnormalized density function with respect to the Lebesgue measure. The hit-and-run, (hybrid) slice sampler and random walk Metropolis algorithm are…
We propose an exact slice sampler for Hierarchical Dirichlet process (HDP) and its associated mixture models (Teh et al., 2006). Although there are existing MCMC algorithms for sampling from the HDP, a slice sampler has been missing from…
In this paper we introduce a new sampling algorithm which has the potential to be adopted as a universal replacement to the Metropolis--Hastings algorithm. It is related to the slice sampler, and motivated by an algorithm which is…
Bayesian inference with nested sampling requires a likelihood-restricted prior sampling method, which draws samples from the prior distribution that exceed a likelihood threshold. For high-dimensional problems, Markov Chain Monte Carlo…
Slice sampling is a well-established Markov chain Monte Carlo method for (approximate) sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a…
We study the Multiple-try Metropolis algorithm using the framework of Poincar\'e inequalities. We describe the Multiple-try Metropolis as an auxiliary variable implementation of a resampling approximation to an ideal Metropolis--Hastings…
Using the framework of weak Poincar\'{e} inequalities, we analyze the convergence properties of deterministic-scan Metropolis-within-Gibbs samplers, an important class of Markov chain Monte Carlo algorithms. Our analysis applies to…
In this paper we firstly derive the weak elliptic Harnack inequality from the generalized capacity condition, the tail estimate of jump measure and the Poincar\'{e} inequality, for any regular Dirichlet form without killing part on a…
Slice Sampling has emerged as a powerful Markov Chain Monte Carlo algorithm that adapts to the characteristics of the target distribution with minimal hand-tuning. However, Slice Sampling's performance is highly sensitive to the…
There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via functional inequalities such as Poincar\'e inequalities. In many situations, Markov chains fail to mix rapidly from a worst-case initialization, yet…
We construct an adaptive independent Metropolis-Hastings sampler that uses a mixture of normals as a proposal distribution. To take full advantage of the potential of adaptive sampling our algorithm updates the mixture of normals…
Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under…
Function approximation and recovery via some sampled data have long been studied in a wide array of applied mathematics and statistics fields. Analytic tools, such as the Poincar\'e inequality, have been handy for estimating the…
We propose an adaptive independent Metropolis--Hastings algorithm with the ability to learn from all previous proposals in the chain except the current location. It is an extension of the independent Metropolis--Hastings algorithm.…
Equilibrium systems evolve according to Detailed Balance (DB). This principe guided development of the Monte-Carlo sampling techniques, of which Metropolis-Hastings (MH) algorithm is the famous representative. It is also known that DB is…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
While established neural network approaches based on restricted Boltzmann machine architectures and Metropolis sampling methods are well suited for symmetric open quantum systems, they result in poor scalability and systematic errors for…
We establish a general theory of optimality for block bootstrap distribution estimation for sample quantiles under a mild strong mixing assumption. In contrast to existing results, we study the block bootstrap for varying numbers of blocks.…
Sampling from multivariate normal distributions, subjected to a variety of restrictions, is a problem that is recurrent in statistics and computing. In the present work, we demonstrate a general framework to efficiently sample a…