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Bayesian Inference

Bayesian Inference
  • Author : William A Link,Richard J Barker
  • Publisher :Unknown
  • Release Date :2009-08-07
  • Total pages :354
  • ISBN : 9780080889801
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Summary : This text is written to provide a mathematically sound but accessible and engaging introduction to Bayesian inference specifically for environmental scientists, ecologists and wildlife biologists. It emphasizes the power and usefulness of Bayesian methods in an ecological context. The advent of fast personal computers and easily available software has simplified the use of Bayesian and hierarchical models . One obstacle remains for ecologists and wildlife biologists, namely the near absence of Bayesian texts written specifically for them. The book includes many relevant examples, is supported by software and examples on a companion website and will become an essential grounding in this approach for students and research ecologists. Engagingly written text specifically designed to demystify a complex subject Examples drawn from ecology and wildlife research An essential grounding for graduate and research ecologists in the increasingly prevalent Bayesian approach to inference Companion website with analytical software and examples Leading authors with world-class reputations in ecology and biostatistics

Bayesian Inference for Stochastic Processes

Bayesian Inference for Stochastic Processes
  • Author : Lyle D. Broemeling
  • Publisher :Unknown
  • Release Date :2017-12-12
  • Total pages :432
  • ISBN : 9781315303581
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Summary : 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

Bayesian Inference
  • Author : Hanns L. Harney
  • Publisher :Unknown
  • Release Date :2013-03-14
  • Total pages :263
  • ISBN : 9783662060063
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Summary : 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
  • Author : Hanns Ludwig Harney
  • Publisher :Unknown
  • Release Date :2016-10-18
  • Total pages :243
  • ISBN : 9783319416441
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Summary : 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.

Bayesian Inference in Statistical Analysis

Bayesian Inference in Statistical Analysis
  • Author : George E. P. Box,George C. Tiao
  • Publisher :Unknown
  • Release Date :2011-01-25
  • Total pages :608
  • ISBN : 9781118031445
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Summary : 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.

Bayesian Inference for Gene Expression and Proteomics

Bayesian Inference for Gene Expression and Proteomics
  • Author : Kim-Anh Do,Peter Müller,Marina Vannucci
  • Publisher :Unknown
  • Release Date :2006-07-24
  • Total pages :437
  • ISBN : 9780521860925
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Summary : Expert overviews of Bayesian methodology, tools and software for multi-platform high-throughput experimentation.

Likelihood and Bayesian Inference

Likelihood and Bayesian Inference
  • Author : Leonhard Held,Daniel Sabanés Bové
  • Publisher :Unknown
  • Release Date :2020-03-31
  • Total pages :402
  • ISBN : 9783662607923
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Summary : 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.

Practical Bayesian Inference

Practical Bayesian Inference
  • Author : Coryn A. L. Bailer-Jones
  • Publisher :Unknown
  • Release Date :2017-04-27
  • Total pages :295
  • ISBN : 9781107192119
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Summary : This book introduces the major concepts of probability and statistics, along with the necessary computational tools, for undergraduates and graduate students.

Perception as Bayesian Inference

Perception as Bayesian Inference
  • Author : David C. Knill,Whitman Richards
  • Publisher :Unknown
  • Release Date :1996-09-13
  • Total pages :229
  • ISBN : 9781316582527
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Summary : Bayesian probability theory has emerged not only as a powerful tool for building computational theories of vision, but also as a general paradigm for studying human visual perception. This 1996 book provides an introduction to and critical analysis of the Bayesian paradigm. Leading researchers in computer vision and experimental vision science describe general theoretical frameworks for modelling vision, detailed applications to specific problems and implications for experimental studies of human perception. The book provides a dialogue between different perspectives both within chapters, which draw on insights from experimental and computational work, and between chapters, through commentaries written by the contributors on each others' work. Students and researchers in cognitive and visual science will find much to interest them in this thought-provoking collection.

Evaluating Great Lakes Bald Eagle Nesting Habitat with Bayesian Inference

Evaluating Great Lakes Bald Eagle Nesting Habitat with Bayesian Inference
  • Author : Teryl G. Grubb
  • Publisher :Unknown
  • Release Date :2003
  • Total pages :10
  • ISBN : MINN:31951D030019195
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Summary : 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.

Bayesian Inference on Multivariate Median and Quantiles

Bayesian Inference on Multivariate Median and Quantiles
  • Author : Indrabati Bhattacharya
  • Publisher :Unknown
  • Release Date :2020
  • Total pages :108
  • ISBN : OCLC:1192484275
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Summary :

Bayesian Inference for Partially Identified Models

Bayesian Inference for Partially Identified Models
  • Author : Paul Gustafson
  • Publisher :Unknown
  • Release Date :2015-04-01
  • Total pages :196
  • ISBN : 9781439869406
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Summary : Bayesian Inference for Partially Identified Models: Exploring the Limits of Limited Data shows how the Bayesian approach to inference is applicable to partially identified models (PIMs) and examines the performance of Bayesian procedures in partially identified contexts. Drawing on his many years of research in this area, the author presents a thorough overview of the statistical theory, properties, and applications of PIMs. The book first describes how reparameterization can assist in computing posterior quantities and providing insight into the properties of Bayesian estimators. It next compares partial identification and model misspecification, discussing which is the lesser of the two evils. The author then works through PIM examples in depth, examining the ramifications of partial identification in terms of how inferences change and the extent to which they sharpen as more data accumulate. He also explains how to characterize the value of information obtained from data in a partially identified context and explores some recent applications of PIMs. In the final chapter, the author shares his thoughts on the past and present state of research on partial identification. This book helps readers understand how to use Bayesian methods for analyzing PIMs. Readers will recognize under what circumstances a posterior distribution on a target parameter will be usefully narrow versus uselessly wide.

Bayesian Statistics for Beginners

Bayesian Statistics for Beginners
  • Author : Therese M. Donovan,Ruth M. Mickey
  • Publisher :Unknown
  • Release Date :2019
  • Total pages :419
  • ISBN : 9780198841296
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Summary : This is an entry-level book on Bayesian statistics written in a casual, and conversational tone. The authors walk a reader through many sample problems step-by-step to provide those with little background in math or statistics with the vocabulary, notation, and understanding of the calculations used in many Bayesian problems.

Bayesian Inference

Bayesian Inference
  • Author : Javier Prieto Tejedor
  • Publisher :Unknown
  • Release Date :2017-11-02
  • Total pages :378
  • ISBN : 9789535135777
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Summary : 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 Statistical Inference

Bayesian Statistical Inference
  • Author : Gudmund R. Iversen
  • Publisher :Unknown
  • Release Date :1984-11
  • Total pages :80
  • ISBN : 0803923287
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Summary : Empirical researchers, for whom Iversen's volume provides an introduction, have generally lacked a grounding in the methodology of Bayesian inference. As a result, applications are few. After outlining the limitations of classical statistical inference, the author proceeds through a simple example to explain Bayes' theorem and how it may overcome these limitations. Typical Bayesian applications are shown, together with the strengths and weaknesses of the Bayesian approach. This monograph thus serves as a companion volume for Henkel's Tests of Significance (QASS vol 4).

Bayesian Methods for Hackers

Bayesian Methods for Hackers
  • Author : Cameron Davidson-Pilon
  • Publisher :Unknown
  • Release Date :2015-09-30
  • Total pages :256
  • ISBN : 9780133902921
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Summary : Master Bayesian Inference through Practical Examples and Computation–Without Advanced Mathematical Analysis Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You’ll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you’ve mastered these techniques, you’ll constantly turn to this guide for the working PyMC code you need to jumpstart future projects. Coverage includes • Learning the Bayesian “state of mind” and its practical implications • Understanding how computers perform Bayesian inference • Using the PyMC Python library to program Bayesian analyses • Building and debugging models with PyMC • Testing your model’s “goodness of fit” • Opening the “black box” of the Markov Chain Monte Carlo algorithm to see how and why it works • Leveraging the power of the “Law of Large Numbers” • Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning • Using loss functions to measure an estimate’s weaknesses based on your goals and desired outcomes • Selecting appropriate priors and understanding how their influence changes with dataset size • Overcoming the “exploration versus exploitation” dilemma: deciding when “pretty good” is good enough • Using Bayesian inference to improve A/B testing • Solving data science problems when only small amounts of data are available Cameron Davidson-Pilon has worked in many areas of applied mathematics, from the evolutionary dynamics of genes and diseases to stochastic modeling of financial prices. His contributions to the open source community include lifelines, an implementation of survival analysis in Python. Educated at the University of Waterloo and at the Independent University of Moscow, he currently works with the online commerce leader Shopify.

Statistical Inference

Statistical Inference
  • Author : Murray Aitkin
  • Publisher :Unknown
  • Release Date :2010-06-02
  • Total pages :254
  • ISBN : 9781420093445
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Summary : Filling a gap in current Bayesian theory, Statistical Inference: An Integrated Bayesian/Likelihood Approach presents a unified Bayesian treatment of parameter inference and model comparisons that can be used with simple diffuse prior specifications. This novel approach provides new solutions to difficult model comparison problems and offers direct Bayesian counterparts of frequentist t-tests and other standard statistical methods for hypothesis testing. After an overview of the competing theories of statistical inference, the book introduces the Bayes/likelihood approach used throughout. It presents Bayesian versions of one- and two-sample t-tests, along with the corresponding normal variance tests. The author then thoroughly discusses the use of the multinomial model and noninformative Dirichlet priors in "model-free" or nonparametric Bayesian survey analysis, before covering normal regression and analysis of variance. In the chapter on binomial and multinomial data, he gives alternatives, based on Bayesian analyses, to current frequentist nonparametric methods. The text concludes with new goodness-of-fit methods for assessing parametric models and a discussion of two-level variance component models and finite mixtures. Emphasizing the principles of Bayesian inference and Bayesian model comparison, this book develops a unique methodology for solving challenging inference problems. It also includes a concise review of the various approaches to inference.

Fundamentals of Nonparametric Bayesian Inference

Fundamentals of Nonparametric Bayesian Inference
  • Author : Subhashis Ghosal,Aad van der Vaart
  • Publisher :Unknown
  • Release Date :2017-06-26
  • Total pages :670
  • ISBN : 9780521878265
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Summary : Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation.

Bayesian Inference on Complicated Data

Bayesian Inference on Complicated Data
  • Author : Niansheng Tang
  • Publisher :Unknown
  • Release Date :2020-07-15
  • Total pages :118
  • ISBN : 9781838803858
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Summary : Due to great applications in various fields, such as social science, biomedicine, genomics, and signal processing, and the improvement of computing ability, Bayesian inference has made substantial developments for analyzing complicated data. This book introduces key ideas of Bayesian sampling methods, Bayesian estimation, and selection of the prior. It is structured around topics on the impact of the choice of the prior on Bayesian statistics, some advances on Bayesian sampling methods, and Bayesian inference for complicated data including breast cancer data, cloud-based healthcare data, gene network data, and longitudinal data. This volume is designed for statisticians, engineers, doctors, and machine learning researchers.

Bayesian inference with INLA

Bayesian inference with INLA
  • Author : Virgilio Gomez-Rubio
  • Publisher :Unknown
  • Release Date :2020-02-20
  • Total pages :316
  • ISBN : 9781351707206
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Summary : 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 Philosophy of Science

Bayesian Philosophy of Science
  • Author : Jan Sprenger,Stephan Hartmann
  • Publisher :Unknown
  • Release Date :2019-08-15
  • Total pages :384
  • ISBN : 9780199672110
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Summary : How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as beingcharacterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in "objective science", Sprenger and Hartmann explain the value of convincing evidence in terms of a cycle of variations on the theme of representing rational degrees ofbelief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference - the leading theory of rationality in social science - with the practice of 21st century science.Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention tomethodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners.