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Gregory P.C. Bayesian Logical Data Analysis for the Physical Sciences. A Comparative Approach with Mathematica Support

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Gregory P.C. Bayesian Logical Data Analysis for the Physical Sciences. A Comparative Approach with Mathematica Support
Cambridge University Press, New York, 2005, 488 pp.
The goal of science is to unlock nature’s secrets. This involves the identification and understanding of nature’s observable structures or patterns. Our understanding comes through the development of theoretical models which are capable of explaining the existing observations as well as making testable predictions. The focus of this book is on what happens at the interface between the predictions of scientific models and the data from the latest experiments. The data are always limited in accuracy and incomplete (we always want more), so we are unable to employ deductive reasoning to prove or disprove the theory. How do we proceed to extend our theoretical framework of understanding in the face of this? Fortunately, a variety of sophisticated mathematical and computational approaches have been developed to help us through this interface, these go under the general heading of statistical inference. Statistical inference provides a means for assessing the plausibility of one or more competing models, and estimating the model parameters and their uncertainties. These topics are commonly referred to as ‘‘data analysis’’ in the jargon of most physicists.
Contents
Preface page
Software support
Role of probability theory in science
Probability theory as extended logic
The how-to of Bayesian inference
Assigning probabilities
Frequentist statistical inference
What is a statistic?
Frequentist hypothesis testing
Maximum entropy probabilities
Bayesian inference with Gaussian errors
Linear model fitting (Gaussian errors)
Nonlinear model fitting
Markov chain Monte Carlo
Bayesian revolution in spectral analysis
Bayesian inference with Poisson sampling
Appendix A Singular value decomposition
Appendix B Discrete Fourier Transforms
Appendix C Difference in two samples
Appendix D Poisson ON/OFF details
Appendix E Multivariate Gaussian from maximum entropy
References
Index
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