Read e-book online Bayesian Logical Data Analysis for the Physical Sciences PDF

By Phil Gregory

ISBN-10: 0521150124

ISBN-13: 9780521150125

Researchers in lots of branches of technological know-how are more and more entering touch with Bayesian statistics or Bayesian likelihood thought. This ebook presents a transparent exposition of the underlying ideas with huge numbers of labored examples and challenge units. It additionally discusses numerical recommendations for imposing the Bayesian calculations, together with Markov Chain Monte-Carlo integration and linear and nonlinear least-squares research obvious from a Bayesian point of view.

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2, we consider the two main inference problems: parameter estimation and model selection. This includes how to specify credible regions for parameters and how to eliminate nuisance parameters through marginalization. We also learn that Bayesian model comparison has a built-in ‘‘Occam’s razor,’’ which automatically penalizes complicated models, assigning them large probabilities only if the complexity of the data justifies the additional complication of the model. We also learn how this penalty arises through marginalization and depends both on the number of parameters and the prior ranges of these parameters.

If the prior density and the likelihood are assigned directly, the global likelihood is an uninteresting normalization constant. The posterior PDF for the parameters is simply proportional to the product of the prior and the likelihood. The use of Bayes’ theorem to determine what one can learn about the values of parameters from data is called parameter estimation, though strictly speaking, Bayesian inference does not provide estimates for parameters. Rather, the Bayesian solution to the parameter estimation problem is the full posterior PDF, pðjD; MÞ, and not just a single point in parameter space.

A; A. Adding any number of impossible propositions to a proposition in a logical sum does not alter the truth value of the proposition. It is like adding a zero to a function; it doesn’t alter the value of the function. 1 Examination of a logic function Any logic function C ¼ fðA; BÞ has only two possible values, and likewise for the independent variables A and B. A logic function with n variables is defined on a discrete space consisting of only m ¼ 2n points. For example, in the case of C ¼ fðA; BÞ, m ¼ 4 points; namely those at which A and B take on the values fTT,TF,FT,FFg.

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Bayesian Logical Data Analysis for the Physical Sciences with Mathematica Support by Phil Gregory

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