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Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…

Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes…

We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with…

Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is…

Sequential Monte Carlo (SMC), also known as particle filters, has been widely accepted as a powerful computational tool for making inference with dynamical systems. A key step in SMC is resampling, which plays the role of steering the…

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster…

Controlled branching processes are stochastic growth population models in which the number of individuals with reproductive capacity in each generation is controlled by a random control function. The purpose of this work is to examine the…

Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or…

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…

Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…

There has been considerable interest in making Bayesian inference more scalable. In big data settings, most literature focuses on reducing the computing time per iteration, with less focused on reducing the number of iterations needed in…

Simulating sampling algorithms with people has proven a useful method for efficiently probing and understanding their mental representations. We propose that the same methods can be used to study the representations of Large Language Models…

The approximation of a high-dimensional vector by a small combination of column vectors selected from a fixed matrix has been actively debated in several different disciplines. In this paper, a sampling approach based on the Monte Carlo…

We develop a scalable multi-step Monte Carlo algorithm for inference under a large class of nonparametric Bayesian models for clustering and classification. Each step is "embarrassingly parallel" and can be implemented using the same Markov…

A system to update estimates from a sequence of probability distributions is presented. The aim of the system is to quickly produce estimates with a user-specified bound on the Monte Carlo error. The estimates are based upon weighted…

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…

Over decades, Markov chain Monte Carlo (MCMC) methods have been widely studied, with a typical application being the quantification of posterior uncertainties in Bayesian system identification of structural dynamic models. To address the…

In this paper we demonstrate that tempering Markov chain Monte Carlo samplers for Bayesian models by recursively subsampling observations without replacement can improve the performance of baseline samplers in terms of effective sample size…

Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…