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Bayesian Inference

Bayesian Inference Book
Author : Hanns L. Harney
Publisher : Springer Science & Business Media
Release : 2003-05-20
ISBN : 9783540003977
Language : En, Es, Fr & De

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Book Description :

Solving a longstanding problem in the physical sciences, this text and reference generalizes Gaussian error intervals to situations in which the data follow distributions other than Gaussian. The text is written at introductory level, with many examples and exercises.

Bayesian Inference

Bayesian Inference Book
Author : Javier Prieto Tejedor
Publisher : BoD – Books on Demand
Release : 2017-11-02
ISBN : 9535135775
Language : En, Es, Fr & De

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Book Description :

The range of Bayesian inference algorithms and their different applications has been greatly expanded since the first implementation of a Kalman filter by Stanley F. Schmidt for the Apollo program. Extended Kalman filters or particle filters are just some examples of these algorithms that have been extensively applied to logistics, medical services, search and rescue operations, or automotive safety, among others. This book takes a look at both theoretical foundations of Bayesian inference and practical implementations in different fields. It is intended as an introductory guide for the application of Bayesian inference in the fields of life sciences, engineering, and economics, as well as a source document of fundamentals for intermediate Bayesian readers.

Bayesian Inference

Bayesian Inference Book
Author : Hanns Ludwig Harney
Publisher : Springer
Release : 2016-10-18
ISBN : 3319416448
Language : En, Es, Fr & De

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Book Description :

This new edition offers a comprehensive introduction to the analysis of data using Bayes rule. It generalizes Gaussian error intervals to situations in which the data follow distributions other than Gaussian. This is particularly useful when the observed parameter is barely above the background or the histogram of multiparametric data contains many empty bins, so that the determination of the validity of a theory cannot be based on the chi-squared-criterion. In addition to the solutions of practical problems, this approach provides an epistemic insight: the logic of quantum mechanics is obtained as the logic of unbiased inference from counting data. New sections feature factorizing parameters, commuting parameters, observables in quantum mechanics, the art of fitting with coherent and with incoherent alternatives and fitting with multinomial distribution. Additional problems and examples help deepen the knowledge. Requiring no knowledge of quantum mechanics, the book is written on introductory level, with many examples and exercises, for advanced undergraduate and graduate students in the physical sciences, planning to, or working in, fields such as medical physics, nuclear physics, quantum mechanics, and chaos.

Perception as Bayesian Inference

Perception as Bayesian Inference Book
Author : David C. Knill,Whitman Richards
Publisher : Cambridge University Press
Release : 1996-09-13
ISBN : 9780521461092
Language : En, Es, Fr & De

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Book Description :

This 1996 book describes an exciting theoretical paradigm for visual perception based on experimental and computational insights.

Bayesian inference with INLA

Bayesian inference with INLA Book
Author : Virgilio Gomez-Rubio
Publisher : CRC Press
Release : 2020-02-20
ISBN : 1351707191
Language : En, Es, Fr & De

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Book Description :

The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods. INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed. Bayesian Inference with INLA provides a description of INLA and its associated R package for model fitting. This book describes the underlying methodology as well as how to fit a wide range of models with R. Topics covered include generalized linear mixed-effects models, multilevel models, spatial and spatio-temporal models, smoothing methods, survival analysis, imputation of missing values, and mixture models. Advanced features of the INLA package and how to extend the number of priors and latent models available in the package are discussed. All examples in the book are fully reproducible and datasets and R code are available from the book website. This book will be helpful to researchers from different areas with some background in Bayesian inference that want to apply the INLA method in their work. The examples cover topics on biostatistics, econometrics, education, environmental science, epidemiology, public health, and the social sciences.

Bayesian Inference for Stochastic Processes

Bayesian Inference for Stochastic Processes Book
Author : Lyle D. Broemeling
Publisher : CRC Press
Release : 2017-12-12
ISBN : 1315303574
Language : En, Es, Fr & De

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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.

Bayesian Inference in Dynamic Econometric Models

Bayesian Inference in Dynamic Econometric Models Book
Author : Luc Bauwens,Michel Lubrano,Jean-François Richard
Publisher : OUP Oxford
Release : 2000-01-06
ISBN : 0191588466
Language : En, Es, Fr & De

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Book Description :

This book contains an up-to-date coverage of the last twenty years advances in Bayesian inference in econometrics, with an emphasis on dynamic models. It shows how to treat Bayesian inference in non linear models, by integrating the useful developments of numerical integration techniques based on simulations (such as Markov Chain Monte Carlo methods), and the long available analytical results of Bayesian inference for linear regression models. It thus covers a broad range of rather recent models for economic time series, such as non linear models, autoregressive conditional heteroskedastic regressions, and cointegrated vector autoregressive models. It contains also an extensive chapter on unit root inference from the Bayesian viewpoint. Several examples illustrate the methods.

Bayesian Inference with Geodetic Applications

Bayesian Inference with Geodetic Applications Book
Author : Karl-Rudolf Koch
Publisher : Springer
Release : 2006-04-11
ISBN : 3540466010
Language : En, Es, Fr & De

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Book Description :

This introduction to Bayesian inference places special emphasis on applications. All basic concepts are presented: Bayes' theorem, prior density functions, point estimation, confidence region, hypothesis testing and predictive analysis. In addition, Monte Carlo methods are discussed since the applications mostly rely on the numerical integration of the posterior distribution. Furthermore, Bayesian inference in the linear model, nonlinear model, mixed model and in the model with unknown variance and covariance components is considered. Solutions are supplied for the classification, for the posterior analysis based on distributions of robust maximum likelihood type estimates, and for the reconstruction of digital images.

Practical Bayesian Inference

Practical Bayesian Inference Book
Author : Coryn A. L. Bailer-Jones
Publisher : Cambridge University Press
Release : 2017-04-27
ISBN : 1108127673
Language : En, Es, Fr & De

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Book Description :

Science is fundamentally about learning from data, and doing so in the presence of uncertainty. This volume is an introduction to the major concepts of probability and statistics, and the computational tools for analysing and interpreting data. It describes the Bayesian approach, and explains how this can be used to fit and compare models in a range of problems. Topics covered include regression, parameter estimation, model assessment, and Monte Carlo methods, as well as widely used classical methods such as regularization and hypothesis testing. The emphasis throughout is on the principles, the unifying probabilistic approach, and showing how the methods can be implemented in practice. R code (with explanations) is included and is available online, so readers can reproduce the plots and results for themselves. Aimed primarily at undergraduate and graduate students, these techniques can be applied to a wide range of data analysis problems beyond the scope of this work.

Bayesian Inference in Statistical Analysis

Bayesian Inference in Statistical Analysis Book
Author : George E. P. Box,George C. Tiao
Publisher : John Wiley & Sons
Release : 2011-01-25
ISBN : 111803144X
Language : En, Es, Fr & De

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Book Description :

Its main objective is to examine the application and relevance of Bayes' theorem to problems that arise in scientific investigation in which inferences must be made regarding parameter values about which little is known a priori. Begins with a discussion of some important general aspects of the Bayesian approach such as the choice of prior distribution, particularly noninformative prior distribution, the problem of nuisance parameters and the role of sufficient statistics, followed by many standard problems concerned with the comparison of location and scale parameters. The main thrust is an investigation of questions with appropriate analysis of mathematical results which are illustrated with numerical examples, providing evidence of the value of the Bayesian approach.

Likelihood and Bayesian Inference

Likelihood and Bayesian Inference Book
Author : Leonhard Held,Daniel Sabanés Bové
Publisher : Springer Nature
Release : 2020-03-31
ISBN : 3662607921
Language : En, Es, Fr & De

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Book Description :

This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book “Applied Statistical Inference” has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications.

Dynamic Programming and Bayesian Inference

Dynamic Programming and Bayesian Inference Book
Author : Mohammad Saber Fallah Nezhad
Publisher : BoD – Books on Demand
Release : 2014-04-29
ISBN : 953511364X
Language : En, Es, Fr & De

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Book Description :

Dynamic programming and Bayesian inference have been both intensively and extensively developed during recent years. Because of these developments, interest in dynamic programming and Bayesian inference and their applications has greatly increased at all mathematical levels. The purpose of this book is to provide some applications of Bayesian optimization and dynamic programming.

Evaluating Great Lakes Bald Eagle Nesting Habitat with Bayesian Inference

Evaluating Great Lakes Bald Eagle Nesting Habitat with Bayesian Inference Book
Author : Teryl G. Grubb
Publisher : Unknown
Release : 2003
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Bayesian inference facilitated structured interpretation of a nonreplicated, experience-based survey of potential nesting habitat for bald eagles (Haliaeetus leucocephalus) along the five Great Lakes shorelines. We developed a pattern recognition (PATREC) model of our aerial search image with six habitat attributes: (a) tree cover, (b) proximity and (c) type/amount of human disturbance, (d) potential foraging habitat/shoreline irregularity, and suitable trees for (e) perching and (f) nesting. Tree cover greater than 10 percent, human disturbance more than 0.8 km away, a ratio of total to linear shoreline distance greater than 2.0, and suitable perch and nest trees were prerequisite for good eagle habitat (having sufficient physical attributes for bald eagle nesting). The estimated probability of good habitat was high (96 percent) when all attributes were optimal, and nonexistent (0 percent) when none of the model attributes were present. Of the 117 active bald eagle nests along the Great Lakes shorelines in 1992, 82 percent were in habitat classified as good. While our PATREC model provides a method for consistent interpretation of subjective surveyor experience, it also facilitates future management of bald eagle nesting habitat along Great Lakes shorelines by providing insight into the number, type, and relative importance of key habitat attributes. This practical application of Bayesian inference demonstrates the technique's advantages for effectively incorporating available expertise, detailing model development processes, enabling exploratory simulations, and facilitating long-term ecosystem monitoring.

An Introduction to Bayesian Inference Methods and Computation

An Introduction to Bayesian Inference  Methods and Computation Book
Author : Nick Heard
Publisher : Springer Nature
Release : 2021-10-17
ISBN : 3030828085
Language : En, Es, Fr & De

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Book Description :

These lecture notes provide a rapid, accessible introduction to Bayesian statistical methods. The course covers the fundamental philosophy and principles of Bayesian inference, including the reasoning behind the prior/likelihood model construction synonymous with Bayesian methods, through to advanced topics such as nonparametrics, Gaussian processes and latent factor models. These advanced modelling techniques can easily be applied using computer code samples written in Python and Stan which are integrated into the main text. Importantly, the reader will learn methods for assessing model fit, and to choose between rival modelling approaches.

Bayesian Inference of State Space Models

Bayesian Inference of State Space Models Book
Author : Kostas Triantafyllopoulos
Publisher : Springer Nature
Release : 2022-05-16
ISBN : 303076124X
Language : En, Es, Fr & De

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Book Description :

Download Bayesian Inference of State Space Models book written by Kostas Triantafyllopoulos, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Probabilized logics related to DSmT and Bayes inference

Probabilized logics related to DSmT and Bayes inference Book
Author : Frederic Dambreville
Publisher : Infinite Study
Release : 2022-05-16
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This work proposes a logical interpretation of the non hybrid Dezert Smarandache Theory (DSmT). As probability is deeply related to a classical semantic, it appears that DSmT relies on an alternative semantic of decision. This semantic is characterized as a probabilized multi-modal logic.

Bayesian Inference and Maximum Entropy Methods in Science and Engineering

Bayesian Inference and Maximum Entropy Methods in Science and Engineering Book
Author : Rainer Fischer,Roland Preuss,Udo von Toussaint
Publisher : A I P Press
Release : 2004-11-19
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

All papers were peer reviewed. Bayesian Inference and Maximum Entropy Methods in Science and Engineering provide a framework for analyzing ill-conditioned data. Maximum Entropy is a theoretical method to draw conclusions when little information is available. Bayesian probability theory provides a formalism for scientific reasoning by analyzing noisy or imcomplete data using prior knowledge.

Bayesian Evaluation of Informative Hypotheses

Bayesian Evaluation of Informative Hypotheses Book
Author : Herbert Hoijtink,Irene Klugkist,Paul Boelen
Publisher : Springer Science & Business Media
Release : 2008-09-08
ISBN : 0387096124
Language : En, Es, Fr & De

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Book Description :

This book provides an overview of the developments in the area of Bayesian evaluation of informative hypotheses that took place since the publication of the ?rst paper on this topic in 2001 [Hoijtink, H. Con?rmatory latent class analysis, model selection using Bayes factors and (pseudo) likelihood ratio statistics. Multivariate Behavioral Research, 36, 563–588]. The current state of a?airs was presented and discussed by the authors of this book during a workshop in Utrecht in June 2007. Here we would like to thank all authors for their participation, ideas, and contributions. We would also like to thank Sophie van der Zee for her editorial e?orts during the construction of this book. Another word of thanks is due to John Kimmel of Springer for his con?dence in the editors and authors. Finally, we would like to thank the Netherlands Organization for Scienti?c Research (NWO) whose VICI grant (453-05-002) awarded to the ?rst author enabled the organization of the workshop, the writing of this book, and continuation of the research with respect to Bayesian evaluation of informative hypotheses.

Hierarchical Linear Models

Hierarchical Linear Models Book
Author : Stephen W. Raudenbush,Anthony S. Bryk
Publisher : SAGE
Release : 2002
ISBN : 9780761919049
Language : En, Es, Fr & De

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Book Description :

Popular in its first edition for its rich, illustrative examples and lucid explanations of the theory and use of hierarchical linear models (HLM), the book has been updated to include: an intuitive introductory summary of the basic procedures for estimation and inference used with HLM models that only requires a minimal level of mathematical sophistication; a new section on multivariate growth models; a discussion of research synthesis or meta-analysis applications; aata analytic advice on centering of level-1 predictors, and new material on plausible value intervals and robust standard estimators.

Bayesian Psychometric Modeling

Bayesian Psychometric Modeling Book
Author : Roy Levy,Robert J. Mislevy
Publisher : CRC Press
Release : 2017-07-28
ISBN : 131535697X
Language : En, Es, Fr & De

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Book Description :

A Single Cohesive Framework of Tools and Procedures for Psychometrics and Assessment Bayesian Psychometric Modeling presents a unified Bayesian approach across traditionally separate families of psychometric models. It shows that Bayesian techniques, as alternatives to conventional approaches, offer distinct and profound advantages in achieving many goals of psychometrics. Adopting a Bayesian approach can aid in unifying seemingly disparate—and sometimes conflicting—ideas and activities in psychometrics. This book explains both how to perform psychometrics using Bayesian methods and why many of the activities in psychometrics align with Bayesian thinking. The first part of the book introduces foundational principles and statistical models, including conceptual issues, normal distribution models, Markov chain Monte Carlo estimation, and regression. Focusing more directly on psychometrics, the second part covers popular psychometric models, including classical test theory, factor analysis, item response theory, latent class analysis, and Bayesian networks. Throughout the book, procedures are illustrated using examples primarily from educational assessments. A supplementary website provides the datasets, WinBUGS code, R code, and Netica files used in the examples.