Related papers: Adaptive Independent Sticky MCMC algorithms
The Monte Carlo simulation (MCS) is a statistical methodology used in a large number of applications. It uses repeated random sampling to solve problems with a probability interpretation to obtain high-quality numerical results. The MCS is…
We propose a new class of structured methods for Monte Carlo (MC) sampling, called DPPMC, designed for high-dimensional nonisotropic distributions where samples are correlated to reduce the variance of the estimator via determinantal point…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
We explore a general framework in Markov chain Monte Carlo (MCMC) sampling where sequential proposals are tried as a candidate for the next state of the Markov chain. This sequential-proposal framework can be applied to various existing…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…
A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and…
The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…
A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good…
The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance…
The adaptive rejection sampling (ARS) algorithm is a universal random generator for drawing samples efficiently from a univariate log-concave target probability density function (pdf). ARS generates independent samples from the target via…
We propose a global optimization algorithm based on the Sequential Monte Carlo (SMC) sampling framework. In this framework, the objective function is normalized to be a probabilistic density function (pdf), based on which a sequence of…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…
Our article is concerned with adaptive sampling schemes for Bayesian inference that update the proposal densities using previous iterates. We introduce a copula based proposal density which is made more efficient by combining it with…
Importance sampling is a Monte Carlo technique for efficiently estimating the likelihood of rare events by biasing the sampling distribution towards the rare event of interest. By drawing weighted samples from a learned proposal…
Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density. This paper contributes to the mathematical understanding of this phenomenon and helps…
Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter $y$. The performance parameter $y$ is random due to the presence of various sources…
We introduce a framework for efficient Markov Chain Monte Carlo (MCMC) algorithms targeting discrete-valued high-dimensional distributions, such as posterior distributions in Bayesian variable selection (BVS) problems. We show that many…