Download or read book Importance Sampling Methods with Multiple Sampling Distributions written by Wentao Li and published by . This book was released on 2013 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complexity of integrands in modern scientific, industrial and financial problems increases rapidly with the development of data collection technologies. Monte Carlo method is widely used for complicated integration. In Monte Carlo integration, it is a natural and flexible method to consider multiple simulation mechanisms instead of one to address different aspects of the integrand. New methods are needed to combine the multiple mechanisms efficiently. Monte Carlo integration methods are reviewed, with focus on importance sampling methods (IS) and sequential Monte Carlo methods (SMC). The former is commonly used for low-dimension problems. The latter is a variation of IS, which has been developed to be a new branch itself in the recent two decades, and promising for high- dimension problems with sequential nature. For IS, techniques for combining multiple proposal distributions have been well developed, including Owen and Zhou (2000) and Tan (2004). Important implementation issues are needed to be resolved, including the allocation of sample budgets and the selection of proposals. A two-stage procedure is proposed to optimize the sample allocation, and although little theoretical investigation has been done for such a two-stage procedure in literatures, its optimality among current approaches is theoretically justified. The choice of the first stage sample size is also discussed through investigating the high order performance of estimators. About the construction of proposals, suggestions are given to approximate the perfect case. For SMC, only the plain vanilla combination of multiple proposals has been used in literatures. A novel SMC filtering scheme is proposed to combine the multiple proposals through the control variates approach in Tan (2004). Control variates are used in both resampling and estimation. The new algorithm is shown to be asymptotically more efficient than the direct use of multiple proposals and control variates. The guidance for selecting multiple proposals and control variates is also given. Numerical studies of the AR(1) model observed with noise and the stochastic volatility model with AR(1) dynamics show that the new algorithm can significantly improve over the bootstrap filter and auxiliary particle filter.
Download or read book Physically Based Rendering written by Matt Pharr and published by Morgan Kaufmann. This book was released on 2010-06-28 with total page 1201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This updated edition describes both the mathematical theory behind a modern photorealistic rendering system as well as its practical implementation. Through the ideas and software in this book, designers will learn to design and employ a full-featured rendering system for creating stunning imagery. Includes a companion site complete with source code for the rendering system described in the book, with support for Windows, OS X, and Linux.
Download or read book Independent Random Sampling Methods written by Luca Martino and published by Springer. This book was released on 2018-03-31 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically addresses the design and analysis of efficient techniques for independent random sampling. Both general-purpose approaches, which can be used to generate samples from arbitrary probability distributions, and tailored techniques, designed to efficiently address common real-world practical problems, are introduced and discussed in detail. In turn, the monograph presents fundamental results and methodologies in the field, elaborating and developing them into the latest techniques. The theory and methods are illustrated with a varied collection of examples, which are discussed in detail in the text and supplemented with ready-to-run computer code. The main problem addressed in the book is how to generate independent random samples from an arbitrary probability distribution with the weakest possible constraints or assumptions in a form suitable for practical implementation. The authors review the fundamental results and methods in the field, address the latest methods, and emphasize the links and interplay between ostensibly diverse techniques.
Download or read book Random Sampling Distributions written by Alan Edward Treloar and published by . This book was released on 1942 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Uncertainty in Engineering written by Louis J. M. Aslett and published by Springer Nature. This book was released on 2022 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners.
Download or read book Sampling Strategies for Natural Resources and the Environment written by Timothy G. Gregoire and published by CRC Press. This book was released on 2007-07-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by renowned experts in the field, Sampling Strategies for Natural Resources and the Environment covers the sampling techniques used in ecology, forestry, environmental science, and natural resources. The book presents methods to estimate aggregate characteristics on a per unit area basis as well as on an elemental basis. In addition to comm
Download or read book Exploring Monte Carlo Methods written by William L. Dunn and published by Elsevier. This book was released on 2022-06-07 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Monte Carlo Methods, Second Edition provides a valuable introduction to the numerical methods that have come to be known as "Monte Carlo." This unique and trusted resource for course use, as well as researcher reference, offers accessible coverage, clear explanations and helpful examples throughout. Building from the basics, the text also includes applications in a variety of fields, such as physics, nuclear engineering, finance and investment, medical modeling and prediction, archaeology, geology and transportation planning. - Provides a comprehensive yet concise treatment of Monte Carlo methods - Uses the famous "Buffon's needle problem" as a unifying theme to illustrate the many aspects of Monte Carlo methods - Includes numerous exercises and useful appendices on: Certain mathematical functions, Bose Einstein functions, Fermi Dirac functions and Watson functions
Download or read book Sequential Monte Carlo Methods in Practice written by Arnaud Doucet and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are revolutionizing the on-line analysis of data in many fileds. They have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques.
Download or read book Importance Sampling and Stratification Techniques for Multivariate Models with Low dimentional Structures written by Yoshihiro Taniguchi and published by . This book was released on 2017 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in finance and risk management involve the computation of quantities related to rare-event analysis. As many financial problems are high-dimensional, the quan- tities of interest rarely have analytical forms and therefore they must be approximated using numerical methods. Plain Monte Carlo (MC) is a versatile simulation-based numer- ical technique suitable to high-dimensional problems as its estimation error converges to zero at a rate independent of the dimension of the problem. The weakness of plain MC is the high computational cost it requires to obtain estimates with small variance. This issue is especially severe for rare-event simulation as a very large number, often over millions, of samples are required to obtain an estimate with reasonable precision. In this thesis, we develop importance sampling (IS) and stratified sampling (SS) schemes for rare-event simulation problems to reduce the variance of the plain MC estimators. The main idea of our approach is to construct effective proposal distributions for IS and partitions of the sample space for SS by exploiting the low-dimensional structures that exist in many financial problems. More specifically, our general approach is to identify a low-dimensional transformation of input variables such that the transformed variables are highly correlated with the output, and then make the rare-event more frequent by twisting the distribution of the transformed variables by using IS and/or SS. In some cases, SS is used instead of IS as SS is shown to give estimators with smaller variance. In other cases, IS and SS are used together to achieve greater variance reduction than when they are used separately. Our proposed methods are applicable to a wide range of problems because they do not assume specific types of problems or distribution of input variables and because their performance does not degrade even in high dimension. Furthermore, our approach serves as a dimension reduction technique, so it enhances the effectiveness of quasi-Monte Carlo sampling methods when combined together. This thesis considers three types of low-dimensional structures in increasing order of generality and develops IS and SS methods under each structural assumption, along with optimal tuning procedures and sampling algorithms under specific distributions. The assumed low-dimensional structures are as follows: the output takes a large value when at least one of the input variables is large; a single-index model where the output depends on the input variables mainly through some one-dimensional projection; and a multi-index model where the output depends on the input mainly through a set of linear combinations. Our numerical experiments find that many financial problems possess one of the assumed low-dimensional structure. When applied to those problems in simulation studies, our proposed methods often give variance reduction factors of over 1,000 with little additional computational costs compared to plain MC.
Download or read book Introductory Statistics written by Douglas S. Shafer and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Learning Statistics with R written by Daniel Navarro and published by Lulu.com. This book was released on 2013-01-13 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Learning Statistics with R" covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software and adopting a light, conversational style throughout. The book discusses how to get started in R, and gives an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book. For more information (and the opportunity to check the book out before you buy!) visit http://ua.edu.au/ccs/teaching/lsr or http://learningstatisticswithr.com
Download or read book Ray Tracing Gems written by Eric Haines and published by Apress. This book was released on 2019-02-25 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a must-have for anyone serious about rendering in real time. With the announcement of new ray tracing APIs and hardware to support them, developers can easily create real-time applications with ray tracing as a core component. As ray tracing on the GPU becomes faster, it will play a more central role in real-time rendering. Ray Tracing Gems provides key building blocks for developers of games, architectural applications, visualizations, and more. Experts in rendering share their knowledge by explaining everything from nitty-gritty techniques that will improve any ray tracer to mastery of the new capabilities of current and future hardware. What you'll learn: The latest ray tracing techniques for developing real-time applications in multiple domains Guidance, advice, and best practices for rendering applications with Microsoft DirectX Raytracing (DXR) How to implement high-performance graphics for interactive visualizations, games, simulations, and more Who this book is for:Developers who are looking to leverage the latest APIs and GPU technology for real-time rendering and ray tracing Students looking to learn about best practices in these areas Enthusiasts who want to understand and experiment with their new GPUs
Download or read book Handbook of Markov Chain Monte Carlo written by Steve Brooks and published by CRC Press. This book was released on 2011-05-10 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their popularization in the 1990s, Markov chain Monte Carlo (MCMC) methods have revolutionized statistical computing and have had an especially profound impact on the practice of Bayesian statistics. Furthermore, MCMC methods have enabled the development and use of intricate models in an astonishing array of disciplines as diverse as fisherie
Download or read book Fault Tolerant Systems written by Israel Koren and published by Elsevier. This book was released on 2010-07-19 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fault-Tolerant Systems is the first book on fault tolerance design with a systems approach to both hardware and software. No other text on the market takes this approach, nor offers the comprehensive and up-to-date treatment that Koren and Krishna provide. This book incorporates case studies that highlight six different computer systems with fault-tolerance techniques implemented in their design. A complete ancillary package is available to lecturers, including online solutions manual for instructors and PowerPoint slides. Students, designers, and architects of high performance processors will value this comprehensive overview of the field. - The first book on fault tolerance design with a systems approach - Comprehensive coverage of both hardware and software fault tolerance, as well as information and time redundancy - Incorporated case studies highlight six different computer systems with fault-tolerance techniques implemented in their design - Available to lecturers is a complete ancillary package including online solutions manual for instructors and PowerPoint slides
Download or read book Lectures on Probability Theory and Mathematical Statistics 3rd Edition written by Marco Taboga and published by Createspace Independent Publishing Platform. This book was released on 2017-12-08 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of 80 short and self-contained lectures covering most of the topics that are usually taught in intermediate courses in probability theory and mathematical statistics. There are hundreds of examples, solved exercises and detailed derivations of important results. The step-by-step approach makes the book easy to understand and ideal for self-study. One of the main aims of the book is to be a time saver: it contains several results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books. The topics covered by the book are as follows. PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions. PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions. PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions. PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart. PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions. PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutsky's Theorem. PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.
Download or read book Introduction to Rare Event Simulation written by James Bucklew and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theory of large deviations. It allows us to view a vast assortment of simulation problems from a unified single perspective.
Download or read book Rare Event Simulation using Monte Carlo Methods written by Gerardo Rubino and published by John Wiley & Sons. This book was released on 2009-03-18 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a probabilistic model, a rare event is an event with a very small probability of occurrence. The forecasting of rare events is a formidable task but is important in many areas. For instance a catastrophic failure in a transport system or in a nuclear power plant, the failure of an information processing system in a bank, or in the communication network of a group of banks, leading to financial losses. Being able to evaluate the probability of rare events is therefore a critical issue. Monte Carlo Methods, the simulation of corresponding models, are used to analyze rare events. This book sets out to present the mathematical tools available for the efficient simulation of rare events. Importance sampling and splitting are presented along with an exposition of how to apply these tools to a variety of fields ranging from performance and dependability evaluation of complex systems, typically in computer science or in telecommunications, to chemical reaction analysis in biology or particle transport in physics. Graduate students, researchers and practitioners who wish to learn and apply rare event simulation techniques will find this book beneficial.
