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Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in…

Markov chain Monte Carlo (MCMC) methods provide consistent of integrals as the number of iterations goes to infinity. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…

In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…

This paper proposes a new theory and methodology to tackle the problem of unifying distributed analyses and inferences on shared parameters from multiple sources, into a single coherent inference. This surprisingly challenging problem…

In this report, we present qualitative analysis of Monte Carlo (MC) dropout method for measuring model uncertainty in neural network (NN) models. We first consider the sources of uncertainty in NNs, and briefly review Bayesian Neural…

Optimizing or sampling complex cost functions of combinatorial optimization problems is a longstanding challenge across disciplines and applications. When employing family of conventional algorithms based on Markov Chain Monte Carlo (MCMC)…

Data analysis in HEP experiments often uses binned likelihood from data and finite Monte Carlo sample. Statistical uncertainty of Monte Carlo sample has been introduced in Frequentist Inference in some literatures, but they are not suitable…

In this paper, we consider a Monte Carlo simulation method (MinMC) that approximates prices and risk measures for a range $\Gamma$ of model parameters at once. The simulation method that we study has recently gained popularity [HS20, FPP22,…

Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…

In a Monte-Carlo test, the observed dataset is fixed, and several resampled or permuted versions of the dataset are generated in order to test a null hypothesis that the original dataset is exchangeable with the resampled/permuted ones.…

Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…

Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed…

In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…

Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…

Monte Carlo (MC) techniques are often used to estimate integrals of a multivariate function using randomly generated samples of the function. In light of the increasing interest in uncertainty quantification and robust design applications…

This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon…

In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such…