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"Monte Carlo"
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Sequential quasi Monte Carlo
We derive and study sequential quasi Monte Carlo (SQMC), a class of algorithms obtained by introducing QMC point sets in particle filtering. SQMC is related to, and may be seen as an extension of, the array‐RQMC algorithm of L'Ecuyer and his colleagues. The complexity of SQMC is O{Nlog(N)}, where N is the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo rate OP(N−1/2). The only requirement to implement SQMC algorithms is the ability to write the simulation of particle xtn given xt−1n as a deterministic function of xt−1n and a fixed number of uniform variates. We show that SQMC is amenable to the same extensions as standard SMC, such as forward smoothing, backward smoothing and unbiased likelihood evaluation. In particular, SQMC may replace SMC within a particle Markov chain Monte Carlo algorithm. We establish several convergence results. We provide numerical evidence that SQMC may significantly outperform SMC in practical scenarios.
Journal Article
Simulation modeling and analysis with Arena
Simulation Modeling and Analysis with Arena is a highly readable textbook which treats the essentials of the Monte Carlo discrete-event simulation methodology, and does so in the context of a popular Arena simulation environment.\" It treats simulation modeling as an in-vitro laboratory that facilitates the understanding of complex systems and experimentation with what-if scenarios in order to estimate their performance metrics. The book contains chapters on the simulation modeling methodology and the underpinnings of discrete-event systems, as well as the relevant underlying probability, statistics, stochastic processes, input analysis, model validation and output analysis. All simulation-related concepts are illustrated in numerous Arena examples, encompassing production lines, manufacturing and inventory systems, transportation systems, and computer information systems in networked settings. · Introduces the concept of discrete event Monte Carlo simulation, the most commonly used methodology for modeling and analysis of complex systems· Covers essential workings of the popular animated simulation language, ARENA, including set-up, design parameters, input data, and output analysis, along with a wide variety of sample model applications from production lines to transportation systems· Reviews elements of statistics, probability, and stochastic processes relevant to simulation modeling* Ample end-of-chapter problems and full Solutions Manual* Includes CD with sample ARENA modeling programs
eBook
Irina Baronova and the Ballets Russes de Monte Carlo
\"Drawing on letters, correspondence, oral histories, and interviews, Baronova's daughter, the actress Victoria Tennant, ... recounts Baronova's dramatic life, from her earliest aspirations to her grueling time on tour to her later years in Australia as a pioneer of the art\"--Dust jacket flap.
Book
A survey of Monte Carlo methods for parameter estimation
Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the maximum likelihood (ML) or maximum a posteriori (MAP) estimators, or by performing a multi-dimensional integration, as in the minimum mean squared error (MMSE) estimators. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and the Monte Carlo (MC) methodology is one feasible approach. MC methods proceed by drawing random samples, either from the desired distribution or from a simpler one, and using them to compute consistent estimators. The most important families of MC algorithms are the Markov chain MC (MCMC) and importance sampling (IS). On the one hand, MCMC methods draw samples from a proposal density, building then an ergodic Markov chain whose stationary distribution is the desired distribution by accepting or rejecting those candidate samples as the new state of the chain. On the other hand, IS techniques draw samples from a simple proposal density and then assign them suitable weights that measure their quality in some appropriate way. In this paper, we perform a thorough review of MC methods for the estimation of static parameters in signal processing applications. A historical note on the development of MC schemes is also provided, followed by the basic MC method and a brief description of the rejection sampling (RS) algorithm, as well as three sections describing many of the most relevant MCMC and IS algorithms, and their combined use. Finally, five numerical examples (including the estimation of the parameters of a chaotic system, a localization problem in wireless sensor networks and a spectral analysis application) are provided in order to demonstrate the performance of the described approaches.
Journal Article
Loser takes all
Bertram had no belief in luck. He was not superstitious. A conspicuously unsuccessful assistant accountant, he was planning to get married for the second time. Quite quietly: St Luke's, Maida Hill, and then two weeks in Bournemouth. But Dreuther, a director of Bertram's firm, whimsically switches wedding and honeymoon to Monte Carlo. Inevitably Bertram visits the Casino. Inevitably he loses. Then suddenly his system starts working.
COUPLING AND CONVERGENCE FOR HAMILTONIAN MONTE CARLO
Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L¹ Wasserstein) distance. The lower bound for the contraction rate is explicit. Global convexity of the potential is not required, and thus multimodal target distributions are included. Explicit quantitative bounds for the number of steps required to approximate the stationary distribution up to a given error ϵ are a direct consequence of contractivity. These bounds show that HMC can overcome diffusive behavior if the duration of the Hamiltonian dynamics is adjusted appropriately.
Journal Article
Theoretical guarantees for approximate sampling from smooth and log-concave densities
Sampling from various kinds of distribution is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, exact sampling from a given distribution is impossible or computationally expensive and, therefore, one needs to resort to approximate sampling strategies. However, there is no well-developed theory providing meaningful non-asymptotic guarantees for the approximate sampling procedures, especially in high dimensional problems. The paper makes some progress in this direction by considering the problem of sampling from a distribution having a smooth and log-concave density defined on ℝρ, for some integer P>0. We establish non-asymptotic bounds for the error of approximating the target distribution by the distribution obtained by the Langevin Monte Carlo method and its variants. We illustrate the effectiveness of the established guarantees with various experiments. Underlying our analysis are insights from the theory of continuous time diffusion processes, which may be of interest beyond the framework of log-concave densities that are considered in the present work.
Journal Article