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Bayesian field theory

Author: Jörg C Lemm
Publisher: Baltimore, Md. : Johns Hopkins University Press, 2003.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Thought-provoking and sure to be controversial, Bayesian Field Theory will be of interest to physicists as well as to other specialists in the rapidly growing number of fields that make use of  Read more...

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Lemm, Jörg C.
Bayesian field theory.
Baltimore, Md. : Johns Hopkins University Press, 2003
(DLC) 2002073958
(OCoLC)50184931
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jörg C Lemm
ISBN: 0801877970 9780801877971
OCLC Number: 52762436
Description: 1 online resource (xix, 411 pages) : illustrations
Contents: Cover; Contents; List of Figures; List of Tables; List of Numerical Case Studies; Acknowledgments; 1 Introduction; 2 Bayesian framework; 2.1 Bayesian models; 2.1.1 Independent, dependent, and hidden variables; 2.1.2 Energies, free energies, and errors; 2.1.3 Bayes' theorem: Posterior, prior, and likelihood; 2.1.4 Predictive density and learning; 2.1.5 Mutual information and learning; 2.1.6 Maximum A Posteriori Approximation (MAP); 2.1.7 Normalization, non-negativity, and specific priors; 2.1.8 Numerical case study: A fair coin?; 2.2 Bayesian decision theory; 2.2.1 Loss and risk. 2.2.2 Loss functions for approximation2.2.3 General loss functions and unsupervised learning; 2.2.4 Log-loss and Maximum A Posteriori Approximation; 2.2.5 Empirical risk minimization; 2.2.6 Interpretations of Occam's razor; 2.2.7 Approaches to empirical learning; 2.3 A priori information; 2.3.1 Controlled, measured, and structural priors; 2.3.2 Noise induced priors; 3 Gaussian prior factors; 3.1 Gaussian prior factor for log-likelihoods; 3.1.1 Lagrange multipliers: Error functional E(L); 3.1.2 Normalization by parameterization: Error functional E(g); 3.1.3 The Hessians H[sub(L)], H[sub(g)]. 3.2 Gaussian prior factor for likelihoods3.2.1 Lagrange multipliers: Error functional E(P); 3.2.2 Normalization by parameterization: Error functional E(z); 3.2.3 The Hessians H[sub(P)], H[sub(z)]; 3.3 Quadratic density estimation and empirical risk minimization; 3.4 Numerical case study: Density estimation with Gaussian specific priors; 3.5 Gaussian prior factors for general field; 3.5.1 The general case; 3.5.2 Square root of P; 3.5.3 Distribution functions; 3.6 Covariances and invariances; 3.6.1 Approximate invariance; 3.6.2 Infinitesimal translations; 3.6.3 Approximate periodicity. 3.6.4 Approximate fractals3.7 Non-zero means; 3.8 Regression; 3.8.1 Gaussian regression; 3.8.2 Exact predictive density; 3.8.3 Gaussian mixture regression (cluster regression); 3.8.4 Support vector machines and regression; 3.8.5 Numerical case study: Approximately invariant regression (AIR); 3.9 Classification; 4 Parameterizing likelihoods: Variational methods; 4.1 General likelihood parameterizations; 4.2 Gaussian priors for likelihood parameters; 4.3 Linear trial spaces; 4.4 Linear regression; 4.5 Mixture models; 4.6 Additive models; 4.7 Product ansatz; 4.8 Decision trees. 4.9 Projection pursuit4.10 Neural networks; 5 Parameterizing priors: Hyperparameters; 5.1 Quenched and annealed prior normalization; 5.2 Saddle point approximations and hyperparameters; 5.2.1 Joint MAP; 5.2.2 Stepwise MAP; 5.2.3 Pointwise approximation; 5.2.4 Marginal posterior and empirical Bayes; 5.2.5 Some variants of stationarity equations; 5.3 Adapting prior, means; 5.3.1 General considerations; 5.3.2 Density estimation and nonparametric boosting; 5.3.3 Unrestricted variation; 5.3.4 Regression; 5.4 Adapting prior covariances; 5.4.1 General case; 5.4.2 Automatic relevance detection.
Responsibility: Jörg C. Lemm.
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There is a considerable amount of interesting discussion on inference generally and, in particular, on Bayesian inference. While a statistician might find the language and point-of-view somewhat Read more...

 
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