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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…

A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable…

Large Language Models (LLMs) are increasingly relied upon for solving complex reasoning tasks in domains such as mathematics, logic, and multi-step question answering. A growing line of work seeks to improve reasoning quality by scaling…

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…

We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…

Consider the problem of approximating a given probability distribution on the cube $[0,1]^n$ via the use of a square lattice discretization with mesh-size $1/N$ and the Metropolis algorithm. Here the dimension $n$ is fixed and we focus for…

Multiple-try Metropolis (MTM) is a popular Markov chain Monte Carlo method with the appealing feature of being amenable to parallel computing. At each iteration, it samples several candidates for the next state of the Markov chain and…

Approximate Bayes Computations (ABC) are used for parameter inference when the likelihood function of the model is expensive to evaluate but relatively cheap to sample from. In particle ABC, an ensemble of particles in the product space of…

Importance sampling and independent Metropolis-Hastings (IMH) are among the fundamental building blocks of Monte Carlo methods. Both require a proposal distribution that globally approximates the target distribution. The Radon-Nikodym…

We show that it is feasible to carry out exact Bayesian inference for non-Gaussian state space models using an adaptive Metropolis Hastings sampling scheme with the likelihood approximated by the particle filter. Furthermore, an adapyive…

In this study, a shell-and-tube heat exchanger (STHX) design based on seven continuous independent design variables is proposed. Delayed Rejection Adaptive Metropolis hasting (DRAM) was utilized as a powerful tool in the Markov chain Monte…

The Rugged Metropolis (RM) algorithm is a biased updating scheme, which aims at directly hitting the most likely configurations in a rugged free energy landscape. Details of the one-variable (RM$_1$) implementation of this algorithm are…

The roulette wheel selection is a critical process in heuristic algorithms, enabling the probabilistic choice of items based on assigned fitness values. It selects an item with a probability proportional to its fitness value. This technique…

This short note is a self-contained and basic introduction to the Metropolis-Hastings algorithm, this ubiquitous tool used for producing dependent simulations from an arbitrary distribution. The document illustrates the principles of the…

Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC…

Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in a…

It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…

The Metropolis-within-Gibbs (MwG) algorithm is a widely used Markov Chain Monte Carlo method for sampling from high-dimensional distributions when exact conditional sampling is intractable. We study MwG with Random Walk Metropolis (RWM)…

Stochastic gradient Markov Chain Monte Carlo algorithms are popular samplers for approximate inference, but they are generally biased. We show that many recent versions of these methods (e.g. Chen et al. (2014)) cannot be corrected using…

We consider versions of the Metropolis algorithm which avoid the inefficiency of rejections. We first illustrate that a natural Uniform Selection Algorithm might not converge to the correct distribution. We then analyse the use of Markov…