Author: Lyle D. Broemeling Publisher: CRC Press ISBN: 1315303582 Category : Mathematics Languages : en Pages : 432
Book Description
This is the first book designed to introduce Bayesian inference procedures for stochastic processes. There are clear advantages to the Bayesian approach (including the optimal use of prior information). Initially, the book begins with a brief review of Bayesian inference and uses many examples relevant to the analysis of stochastic processes, including the four major types, namely those with discrete time and discrete state space and continuous time and continuous state space. The elements necessary to understanding stochastic processes are then introduced, followed by chapters devoted to the Bayesian analysis of such processes. It is important that a chapter devoted to the fundamental concepts in stochastic processes is included. Bayesian inference (estimation, testing hypotheses, and prediction) for discrete time Markov chains, for Markov jump processes, for normal processes (e.g. Brownian motion and the Ornstein–Uhlenbeck process), for traditional time series, and, lastly, for point and spatial processes are described in detail. Heavy emphasis is placed on many examples taken from biology and other scientific disciplines. In order analyses of stochastic processes, it will use R and WinBUGS. Features: Uses the Bayesian approach to make statistical Inferences about stochastic processes The R package is used to simulate realizations from different types of processes Based on realizations from stochastic processes, the WinBUGS package will provide the Bayesian analysis (estimation, testing hypotheses, and prediction) for the unknown parameters of stochastic processes To illustrate the Bayesian inference, many examples taken from biology, economics, and astronomy will reinforce the basic concepts of the subject A practical approach is implemented by considering realistic examples of interest to the scientific community WinBUGS and R code are provided in the text, allowing the reader to easily verify the results of the inferential procedures found in the many examples of the book Readers with a good background in two areas, probability theory and statistical inference, should be able to master the essential ideas of this book.
Author: Andrew Gelman Publisher: CRC Press ISBN: 1439840954 Category : Mathematics Languages : en Pages : 677
Book Description
Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Author: Christiane Fuchs Publisher: Springer Science & Business Media ISBN: 3642259693 Category : Mathematics Languages : en Pages : 439
Book Description
Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.
Author: Osvaldo A. Martin Publisher: CRC Press ISBN: 1000520048 Category : Computers Languages : en Pages : 420
Book Description
Bayesian Modeling and Computation in Python aims to help beginner Bayesian practitioners to become intermediate modelers. It uses a hands on approach with PyMC3, Tensorflow Probability, ArviZ and other libraries focusing on the practice of applied statistics with references to the underlying mathematical theory. The book starts with a refresher of the Bayesian Inference concepts. The second chapter introduces modern methods for Exploratory Analysis of Bayesian Models. With an understanding of these two fundamentals the subsequent chapters talk through various models including linear regressions, splines, time series, Bayesian additive regression trees. The final chapters include Approximate Bayesian Computation, end to end case studies showing how to apply Bayesian modelling in different settings, and a chapter about the internals of probabilistic programming languages. Finally the last chapter serves as a reference for the rest of the book by getting closer into mathematical aspects or by extending the discussion of certain topics. This book is written by contributors of PyMC3, ArviZ, Bambi, and Tensorflow Probability among other libraries.
Author: Simo Särkkä Publisher: Cambridge University Press ISBN: 110703065X Category : Computers Languages : en Pages : 255
Book Description
A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
Author: İhsan Bucak Publisher: BoD – Books on Demand ISBN: 1837693560 Category : Mathematics Languages : en Pages : 90
Book Description
In an era where data is abundant and computational power is soaring, Bayesian Inference - Recent Trends emerges as an essential guide to understanding and applying Bayesian methods in various scientific and technological domains. This book uniquely blends theoretical rigor with practical insights, showcasing the latest advancements and applications of Bayesian inference. • Discover the renaissance of Bayesian inference and its vital role in modern-day statistical analysis and prediction. • Explore the depth of hidden Markov models and their power in inferring hidden states and transitions in stochastic systems. • Dive into the complexity of nested sampling and its effectiveness in parameter estimation, particularly in signal processing. • Examine the precision of naive Bayes algorithms in news classification, a critical task in the digital information age. This book is an invaluable resource for anyone interested in the intersection of statistics, machine learning, and data science. It offers a unique perspective on Bayesian inference, revealing its potential to provide robust solutions in an increasingly data-driven world. Whether you are a seasoned researcher, a budding scientist, or a curious enthusiast, Bayesian Inference - Recent Trends is your gateway to understanding and leveraging the power of Bayesian methods in the ever-evolving landscape of data analysis.
Author: D. Costantini Publisher: Springer Science & Business Media ISBN: 940115712X Category : Mathematics Languages : en Pages : 277
Book Description
The book is a collection of essays on various issues in philosophy of science, with special emphasis on the foundations of probability and statistics, and quantum mechanics. The main topics, addressed by some of the most outstanding researchers in the field, are subjective probability, Bayesian statistics, probability kinematics, causal decision making, probability and realism in quantum mechanics.
Author: Kostas Triantafyllopoulos Publisher: Springer Nature ISBN: 303076124X Category : Mathematics Languages : en Pages : 503
Book Description
Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a comprehensive introduction to Bayesian estimation and forecasting for state space models. The celebrated Kalman filter, with its numerous extensions, takes centre stage in the book. Univariate and multivariate models, linear Gaussian, non-linear and non-Gaussian models are discussed with applications to signal processing, environmetrics, economics and systems engineering. Over the past years there has been a growing literature on Bayesian inference of state space models, focusing on multivariate models as well as on non-linear and non-Gaussian models. The availability of time series data in many fields of science and industry on the one hand, and the development of low-cost computational capabilities on the other, have resulted in a wealth of statistical methods aimed at parameter estimation and forecasting. This book brings together many of these methods, presenting an accessible and comprehensive introduction to state space models. A number of data sets from different disciplines are used to illustrate the methods and show how they are applied in practice. The R package BTSA, created for the book, includes many of the algorithms and examples presented. The book is essentially self-contained and includes a chapter summarising the prerequisites in undergraduate linear algebra, probability and statistics. An up-to-date and complete account of state space methods, illustrated by real-life data sets and R code, this textbook will appeal to a wide range of students and scientists, notably in the disciplines of statistics, systems engineering, signal processing, data science, finance and econometrics. With numerous exercises in each chapter, and prerequisite knowledge conveniently recalled, it is suitable for upper undergraduate and graduate courses.
Author: Tasha Fairfield Publisher: Cambridge University Press ISBN: 1108421644 Category : Political Science Languages : en Pages : 683
Book Description
Provides guidance for Bayesian updating in case study, process-tracing, and comparative research, in order to refine intuition and improve inferences from qualitative evidence.
Author: Dani Gamerman Publisher: CRC Press ISBN: 148229642X Category : Mathematics Languages : en Pages : 342
Book Description
While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simul
Author: Lyle D. Broemeling
Author: Andrew Gelman
Author: Christiane Fuchs
Author: Osvaldo A. Martin
Author: Simo Särkkä
Author: İhsan Bucak
Author: D. Costantini
Author: Kostas Triantafyllopoulos
Author: Tasha Fairfield
Author: Dani Gamerman