Perfect Simulation

Author: Mark L. Huber
Publisher: CRC Press
ISBN: 1482232456
Format: PDF, ePub, Mobi
Download Now
Exact sampling, specifically coupling from the past (CFTP), allows users to sample exactly from the stationary distribution of a Markov chain. During its nearly 20 years of existence, exact sampling has evolved into perfect simulation, which enables high-dimensional simulation from interacting distributions. Perfect Simulation illustrates the application of perfect simulation ideas and algorithms to a wide range of problems. The book is one of the first to bring together research on simulation from statistics, physics, finance, computer science, and other areas into a unified framework. You will discover the mechanisms behind creating perfect simulation algorithms for solving an array of problems. The author describes numerous protocol methodologies for designing algorithms for specific problems. He first examines the commonly used acceptance/rejection (AR) protocol for creating perfect simulation algorithms. He then covers other major protocols, including CFTP; the Fill, Machida, Murdoch, and Rosenthal (FMMR) method; the randomness recycler; retrospective sampling; and partially recursive AR, along with multiple variants of these protocols. The book also shows how perfect simulation methods have been successfully applied to a variety of problems, such as Markov random fields, permutations, stochastic differential equations, spatial point processes, Bayesian posteriors, combinatorial objects, and Markov processes.

Statistical Inference and Simulation for Spatial Point Processes

Author: Jesper Moller
Publisher: CRC Press
ISBN: 9780203496930
Format: PDF, Docs
Download Now
Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.

Mean Field Simulation for Monte Carlo Integration

Author: Pierre Del Moral
Publisher: CRC Press
ISBN: 1466504056
Format: PDF, ePub, Docs
Download Now
In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Markov chain Monte Carlo models; bootstrapping methods; ensemble Kalman filters; and interacting particle filters. Mean Field Simulation for Monte Carlo Integration presents the first comprehensive and modern mathematical treatment of mean field particle simulation models and interdisciplinary research topics, including interacting jumps and McKean-Vlasov processes, sequential Monte Carlo methodologies, genetic particle algorithms, genealogical tree-based algorithms, and quantum and diffusion Monte Carlo methods. Along with covering refined convergence analysis on nonlinear Markov chain models, the author discusses applications related to parameter estimation in hidden Markov chain models, stochastic optimization, nonlinear filtering and multiple target tracking, stochastic optimization, calibration and uncertainty propagations in numerical codes, rare event simulation, financial mathematics, and free energy and quasi-invariant measures arising in computational physics and population biology. This book shows how mean field particle simulation has revolutionized the field of Monte Carlo integration and stochastic algorithms. It will help theoretical probability researchers, applied statisticians, biologists, statistical physicists, and computer scientists work better across their own disciplinary boundaries.

Introduction to Time Series Modeling

Author: Genshiro Kitagawa
Publisher: CRC Press
ISBN: 9781584889229
Format: PDF, ePub, Mobi
Download Now
In time series modeling, the behavior of a certain phenomenon is expressed in relation to the past values of itself and other covariates. Since many important phenomena in statistical analysis are actually time series and the identification of conditional distribution of the phenomenon is an essential part of the statistical modeling, it is very important and useful to learn fundamental methods of time series modeling. Illustrating how to build models for time series using basic methods, Introduction to Time Series Modeling covers numerous time series models and the various tools for handling them. The book employs the state-space model as a generic tool for time series modeling and presents convenient recursive filtering and smoothing methods, including the Kalman filter, the non-Gaussian filter, and the sequential Monte Carlo filter, for the state-space models. Taking a unified approach to model evaluation based on the entropy maximization principle advocated by Dr. Akaike, the author derives various methods of parameter estimation, such as the least squares method, the maximum likelihood method, recursive estimation for state-space models, and model selection by the Akaike information criterion (AIC). Along with simulation methods, he also covers standard stationary time series models, such as AR and ARMA models, as well as nonstationary time series models, including the locally stationary AR model, the trend model, the seasonal adjustment model, and the time-varying coefficient AR model. With a focus on the description, modeling, prediction, and signal extraction of times series, this book provides basic tools for analyzing time series that arise in real-world problems. It encourages readers to build models for their own real-life problems.

Practical Risk Theory for Actuaries

Author: C.D. Daykin
Publisher: CRC Press
ISBN: 9780412428500
Format: PDF
Download Now
This classic textbook covers all aspects of risk theory in a practical way. It builds on from the late R.E. Beard's extremely popular book Risk Theory, but features more emphasis on simulation and modeling and on the use of risk theory as a practical tool. Practical Risk Theory is a textbook for practicing and student actuaries on the practical aspects of stochastic modeling of the insurance business. It has its roots in the classical theory of risk but introduces many new elements that are important in managing the insurance business but are usually ignored in the classical theory. The authors avoid overcomplicated mathematics and provide an abundance of diagrams.

Statistical Methods for Stochastic Differential Equations

Author: Mathieu Kessler
Publisher: CRC Press
ISBN: 1439849765
Format: PDF, Docs
Download Now
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a spectrum of estimation methods, including nonparametric estimation as well as parametric estimation based on likelihood methods, estimating functions, and simulation techniques. Two chapters are devoted to high-frequency data. Multivariate models are also considered, including partially observed systems, asynchronous sampling, tests for simultaneous jumps, and multiscale diffusions. Statistical Methods for Stochastic Differential Equations is useful to the theoretical statistician and the probabilist who works in or intends to work in the field, as well as to the applied statistician or financial econometrician who needs the methods to analyze biological or financial time series.

Gaussian Markov Random Fields

Author: Havard Rue
Publisher: CRC Press
ISBN: 9780203492024
Format: PDF, ePub, Mobi
Download Now
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.

Randomised Response Adaptive Designs in Clinical Trials

Author: Anthony C Atkinson
Publisher: CRC Press
ISBN: 1584886935
Format: PDF, Mobi
Download Now
Randomised Response-Adaptive Designs in Clinical Trials presents methods for the randomised allocation of treatments to patients in sequential clinical trials. Emphasizing the practical application of clinical trial designs, the book is designed for medical and applied statisticians, clinicians, and statisticians in training. After introducing clinical trials in drug development, the authors assess a simple adaptive design for binary responses without covariates. They discuss randomisation and covariate balance in normally distributed responses and cover many important response-adaptive designs for binary responses. The book then develops response-adaptive designs for continuous and longitudinal responses, optimum designs with covariates, and response-adaptive designs with covariates. It also covers response-adaptive designs that are derived by optimising an objective function subject to constraints on the variance of estimated parametric functions. The concluding chapter explores future directions in the development of adaptive designs.

Robust Cluster Analysis and Variable Selection

Author: Gunter Ritter
Publisher: CRC Press
ISBN: 1439857962
Format: PDF, Docs
Download Now
Clustering remains a vibrant area of research in statistics. Although there are many books on this topic, there are relatively few that are well founded in the theoretical aspects. In Robust Cluster Analysis and Variable Selection, Gunter Ritter presents an overview of the theory and applications of probabilistic clustering and variable selection, synthesizing the key research results of the last 50 years. The author focuses on the robust clustering methods he found to be the most useful on simulated data and real-time applications. The book provides clear guidance for the varying needs of both applications, describing scenarios in which accuracy and speed are the primary goals. Robust Cluster Analysis and Variable Selection includes all of the important theoretical details, and covers the key probabilistic models, robustness issues, optimization algorithms, validation techniques, and variable selection methods. The book illustrates the different methods with simulated data and applies them to real-world data sets that can be easily downloaded from the web. This provides you with guidance in how to use clustering methods as well as applicable procedures and algorithms without having to understand their probabilistic fundamentals.

Statistical Methods for Spatio Temporal Systems

Author: Barbel Finkenstadt
Publisher: CRC Press
ISBN: 1420011057
Format: PDF, ePub
Download Now
Statistical Methods for Spatio-Temporal Systems presents current statistical research issues on spatio-temporal data modeling and will promote advances in research and a greater understanding between the mechanistic and the statistical modeling communities. Contributed by leading researchers in the field, each self-contained chapter starts with an introduction of the topic and progresses to recent research results. Presenting specific examples of epidemic data of bovine tuberculosis, gastroenteric disease, and the U.K. foot-and-mouth outbreak, the first chapter uses stochastic models, such as point process models, to provide the probabilistic backbone that facilitates statistical inference from data. The next chapter discusses the critical issue of modeling random growth objects in diverse biological systems, such as bacteria colonies, tumors, and plant populations. The subsequent chapter examines data transformation tools using examples from ecology and air quality data, followed by a chapter on space-time covariance functions. The contributors then describe stochastic and statistical models that are used to generate simulated rainfall sequences for hydrological use, such as flood risk assessment. The final chapter explores Gaussian Markov random field specifications and Bayesian computational inference via Gibbs sampling and Markov chain Monte Carlo, illustrating the methods with a variety of data examples, such as temperature surfaces, dioxin concentrations, ozone concentrations, and a well-established deterministic dynamical weather model.