Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.
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Editorial Reviews
Review
"All researchers and scientists who are interested in the Bayesian scientific paradigm can benefit greatly from the examples and illustrations here. It is a welcome addition to the vast literature on Bayesian inference."
Sreenivasan Ravi, University of Mysore, Manasagangotri
Sreenivasan Ravi, University of Mysore, Manasagangotri
Book Description
Increasingly, researchers in many branches of science are coming into contact with Bayesian statistics or Bayesian probability theory. This book provides a clear exposition of the underlying concepts with large numbers of worked examples and problem sets. The book also discusses numerical techniques for implementing the Bayesian calculations, including Markov Chain Monte-Carlo integration and linear and nonlinear least-squares analysis seen from a Bayesian pe rspective. Background material is provided in appendices and supporting Mathematica notebooks are available. Suitable for upper-undergraduates, graduate students, or any serious researcher in physical sciences or engineering.
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16 of 16 people found the following review helpful:
5.0 out of 5 stars
Excellent and practical Bayesian primer,
This review is from: Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica® Support (Hardcover)
Phil Gregory has managed to condense the most important aspects of Bayesian probability and data analysis into a book that is actually rather practical. This book will give you a solid Bayesian understanding of probability, starting with first principles (Cox's desiderata), continuing to Bayes theorem, an introduction to common probability distributions, and concluding with rather advanced numerical techniques such as tempered Markov Chain Monte Carlo. The book is geared towards a reader who will use Mathematica to work through examples, but can be successfully used by others who prefer cheaper and more practical computational frameworks. It's not a flawless book by any means---first of all, although the book purports to cover frequentist alternatives to Bayesian methods, the frequentist coverage is very shallow and inadequate to give the reader enough background to either use or really understand frequentist usage. The chapter on maximum entropy techniques is woefully incomplete, and doesn't include general Jeffreys priors (derived from the Fisher information) or really explain the various issues associated with defining the entropy for continuous distributions. The section on deriving priors with uncertain constraints actually doesn't give an answer to how to handle uncertain constraints! But on the plus side this book answered a number of questions that have long puzzled me, such as why frequentists marginalize over nuisance parameters by minimizing the likelihood function with respect to them instead of integrating over them (it's a dodge that only really works for Gaussian-like distributions), and how to handle the enormous numbers of parameters that Bayesian calculations can generate through the use of Markov Chain Monte Carlos. I wish the book had been longer or more detailed, but if you want to learn Bayesian analysis and don't care much about understanding frequentist statistics, this is an excellent place to start.
3 of 3 people found the following review helpful:
5.0 out of 5 stars
Don't think twice,
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This review is from: Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica® Support (Paperback)
Nicely written. Clear and concise. Chapter 12 contains a great introduction to Monte Carlo methods, the best I ever had read for novice practitioners. Buy it!
5.0 out of 5 stars
Memoirs found in a restroom: It's logical Captain,
By Bvalltu (United States) - See all my reviews
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This review is from: Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica® Support (Paperback)
Very nice book. Even if you don't use Mathematica (I only use it on occasion), this is a very insightful book on Bayesian inference. The future is Bayesian, this book will help guide you to that future. Yes, there are a lot of other books on Bayesian inference on the market, but I really think this has something to offer and is complementary to many of the other books. Being a physicist, Gregory pays attention to Jaynes' brilliant work (especially since he was introduced to it when he found the PhD dissertation by Jaynes' student, Bretthorst, in a restroom one day!), which is light years ahead of its time. If you want to be an ace data analyst/statistician, this book will give you put you in with the front runners.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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joint credible region, robust parameter errors, frequentist statistical inference, following line computes, hypothetical repeats, spectral line problem, median subtraction, strong syllogisms, linear model fitting, global likelihood, frequentist hypothesis testing, spectral line data, ith data value, model parameter errors, prior range, prior boundaries, control system error, timing residuals, relevant prior information, iterative linearization, most probable set, credible regions, most conservative choice, model selection problem, frequentist statistics Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Central Limit Theorem, Combining Equations, Fourier Power Spectral Density, Substituting Equations, Bretthorst's Bayesian, Maximum Entropy Data Consultants, Iteration Figure, Substitution of Equations, Discrete Fourier Transform, Generalized Lomb-Scargle, Uniform Jeffreys, American Institute of Physics, Following Equation, Frequency Frequency Lomb-Scargle Periodogram Bayesian Lomb-Scargle, Fast Fourier Transform, Tom Loredo, Claude Shannon, Frequency Frequency Figure, World Cup, Metropolis-Hastings Markov Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
joint credible region, robust parameter errors, frequentist statistical inference, following line computes, hypothetical repeats, spectral line problem, median subtraction, strong syllogisms, linear model fitting, global likelihood, frequentist hypothesis testing, spectral line data, ith data value, model parameter errors, prior range, prior boundaries, control system error, timing residuals, relevant prior information, iterative linearization, most probable set, credible regions, most conservative choice, model selection problem, frequentist statistics Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Central Limit Theorem, Combining Equations, Fourier Power Spectral Density, Substituting Equations, Bretthorst's Bayesian, Maximum Entropy Data Consultants, Iteration Figure, Substitution of Equations, Discrete Fourier Transform, Generalized Lomb-Scargle, Uniform Jeffreys, American Institute of Physics, Following Equation, Frequency Frequency Lomb-Scargle Periodogram Bayesian Lomb-Scargle, Fast Fourier Transform, Tom Loredo, Claude Shannon, Frequency Frequency Figure, World Cup, Metropolis-Hastings Markov Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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