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Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…

Artificial Intelligence · Computer Science 2013-04-15 Alan Bundy

Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting…

Optimization and Control · Mathematics 2024-09-17 Amon Lahr , Filip Tronarp , Nathanael Bosch , Jonathan Schmidt , Philipp Hennig , Melanie N. Zeilinger

Causal effect estimation is important for many tasks in the natural and social sciences. We design algorithms for the continuous partial identification problem: bounding the effects of multivariate, continuous treatments when unmeasured…

Machine Learning · Statistics 2023-05-18 Kirtan Padh , Jakob Zeitler , David Watson , Matt Kusner , Ricardo Silva , Niki Kilbertus

Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…

Machine Learning · Statistics 2022-06-08 Yi-An Ma , Yuansi Chen , Chi Jin , Nicolas Flammarion , Michael I. Jordan

Quasi-Monte Carlo (QMC) methods are being adopted in statistical applications due to the increasingly challenging nature of numerical integrals that are now routinely encountered. For integrands with $d$-dimensions and derivatives of order…

Computation · Statistics 2016-04-04 Chris. J. Oates , Mark Girolami

Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…

Programming Languages · Computer Science 2022-04-15 Maria I. Gorinova

Probabilistic integration provides a criterion for stopping a simulation when a specified error tolerance is satisfied with high confidence. We comment on some of the modeling assumptions and implementation issues involved in designing an…

Numerical Analysis · Mathematics 2018-12-06 Fred J. Hickernell , R. Jagadeeswaran

Computation in the past decades has been driven by deterministic computers based on classical deterministic bits. Recently, alternative computing paradigms and domain-based computing like quantum computing and probabilistic computing have…

Emerging Technologies · Computer Science 2021-10-01 Jan Kaiser , Risi Jaiswal , Behtash Behin-Aein , Supriyo Datta

Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…

Computation · Statistics 2025-05-15 Abdul-Lateef Haji-Ali , Marcelo Pereyra , Luke Shaw , Konstantinos Zygalakis

We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…

Machine Learning · Computer Science 2015-12-03 Edward Meeds , Max Welling

Weak convergence of various general functionals of partial sums of dependent random variables to stochastic integral now play a major role in the modern statistics theory. In this paper, we obtain the weak convergence of various general…

Probability · Mathematics 2010-08-03 Zheng-Yan Lin , Han-Chao Wang

The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…

Statistical Mechanics · Physics 2007-05-23 Jian-Sheng Wang

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…

Methodology · Statistics 2017-02-13 Edward L. Ionides , Carles Breto , Joonha Park , Richard A. Smith , Aaron A. King

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…

Computation · Statistics 2018-09-28 Bochao Jia

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…

High Energy Physics - Experiment · Physics 2023-09-28 Shilin Liu , Clark McGrew

Since the work of Ferrenberg et al.[PRL 69, (1992)] some pseudo random number generators are known to yield wrong results in cluster Monte Carlo simulations. In this contribution the fundamental mechanism behind this failure is discussed.…

Statistical Mechanics · Physics 2007-05-23 Stephan Mertens , Heiko Bauke

Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the…

Statistics Theory · Mathematics 2009-09-29 James M. Flegal , Murali Haran , Galin L. Jones

In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…

Condensed Matter · Physics 2011-05-21 M. P. Nightingale , C. J. Umrigar

Equality-constrained models naturally arise in problems in which measurements are taken at different levels of resolution. The challenge in this setting is that the models usually induce a joint distribution which is intractable. Resorting…

Computation · Statistics 2025-04-28 Shenggang Hu , Hongsheng Dai , Fanlin Meng , Louis Aslett , Murray Pollock , Gareth O. Roberts

In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…

Applications · Statistics 2013-06-26 Ilya Gertsbakh , Eyal Neuman , Radislav Vaisman