This highly accessible and innovative text with supporting web site uses Excel (R) to teach the core concepts of econometrics without advanced mathematics. It enables students to use Monte Carlo ...simulations in order to understand the data generating process and sampling distribution. Intelligent repetition of concrete examples effectively conveys the properties of the ordinary least squares (OLS) estimator and the nature of heteroskedasticity and autocorrelation. Coverage includes omitted variables, binary response models, basic time series, and simultaneous equations. The authors teach students how to construct their own real-world data sets drawn from the internet, which they can analyze with Excel (R) or with other econometric software. The accompanying web site with text support can be found at www.wabash.edu/econometrics.
Sequential quasi Monte Carlo Gerber, Mathieu; Chopin, Nicolas
Journal of the Royal Statistical Society. Series B, Statistical methodology,
June 2015, Volume:
77, Issue:
3
Journal Article
Peer reviewed
Open access
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.
This new and updated edition deals with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics, statistical mechanics, and related fields. After ...briefly recalling essential background in statistical mechanics and probability theory, it gives a succinct overview of simple sampling methods. The concepts behind the simulation algorithms are explained comprehensively, as are the techniques for efficient evaluation of system configurations generated by simulation. It contains many applications, examples, and exercises to help the reader and provides many new references to more specialized literature. This edition includes a brief overview of other methods of computer simulation and an outlook for the use of Monte Carlo simulations in disciplines beyond physics. This is an excellent guide for graduate students and researchers who use computer simulations in their research. It can be used as a textbook for graduate courses on computer simulations in physics and related disciplines.
This current and comprehensive book provides an updated treatment of molecular gas dynamics topics for aerospace engineers, or anyone researching high-temperature gas flows for hypersonic vehicles ...and propulsion systems. It demonstrates how the areas of quantum mechanics, kinetic theory, and statistical mechanics can combine in order to facilitate the study of nonequilibrium processes of internal energy relaxation and chemistry. All of these theoretical ideas are used to explain the direct simulation Monte Carlo (DSMC) method, a numerical technique based on molecular simulation. Because this text provides comprehensive coverage of the physical models available for use in the DSMC method, in addition to the equations and algorithms required to implement the DSMC numerical method, readers will learn to solve nonequilibrium flow problems and perform computer simulations, and obtain a more complete understanding of various physical modeling options for DSMC than is available in other texts.
Defining accurate and compact trial wavefunctions leading to small statistical and fixed-node errors in quantum Monte Carlo (QMC) calculations is still a challenging problem. Here we propose to make ...use of selected configuration interaction (CI) expansions obtained by selecting the most important determinants through a perturbative criterion. A major advantage with respect to truncated CASSCF wavefunctions or CI expansions limited to a maximum number of excitations (e.g, CISD) is that much smaller expansions can be considered (many unessential determinants are avoided), an important practical point for efficient QMC calculations. The most important determinants entering first during the selection process (hierarchical construction) the main features of the nodal structure of the wavefunction can be expected to be obtained with a moderate number of determinants. Thanks to this property, the delicate problem of optimizing in a Monte Carlo framework the numerous linear and (or) nonlinear parameters of the determinantal part of the trial wavefunction could be avoided. As a first numerical example, the calculation of the ground-state energy of the oxygen atom is presented. The best DMC value reported so far is obtained.
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.
•The most popular sampling techniques for model updating are presented.•Methods, numerical implementations and tuning strategies are provided.•Examples with increase complexity are used to present ...and evaluate the samplers.•The DLR-AIRMOD model updating problem is used as a benchmark for the different solvers.•Algorithms, codes and tutorials are provided as additional material.
This tutorial paper reviews the use of advanced Monte Carlo sampling methods in the context of Bayesian model updating for engineering applications. Markov Chain Monte Carlo, Transitional Markov Chain Monte Carlo, and Sequential Monte Carlo methods are introduced, applied to different case studies and finally their performance is compared. For each of these methods, numerical implementations and their settings are provided.
Three case studies with increased complexity and challenges are presented showing the advantages and limitations of each of the sampling techniques under review. The first case study presents the parameter identification for a spring-mass system under a static load. The second case study presents a 2-dimensional bi-modal posterior distribution and the aim is to observe the performance of each of these sampling techniques in sampling from such distribution. Finally, the last case study presents the stochastic identification of the model parameters of a complex and non-linear numerical model based on experimental data.
The case studies presented in this paper consider the recorded data set as a single piece of information which is used to make inferences and estimations on time-invariant model parameters.
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