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|a UAMI
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|a Lemm, Jörg C.
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|a Bayesian field theory /
|c Jörg C. Lemm.
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|a Baltimore, Md. :
|b Johns Hopkins University Press,
|c 2003.
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| 300 |
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|a 1 online resource (xix, 411 pages) :
|b illustrations
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|a text
|b txt
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|a online resource
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|a Includes bibliographical references (pages 365-402) and index.
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|a Print version record.
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|a 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.
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|a 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)].
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|a 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.
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|a 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.
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|a 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.
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|a eBooks on EBSCOhost
|b EBSCO eBook Subscription Academic Collection - Worldwide
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| 650 |
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0 |
|a Bayesian field theory.
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| 650 |
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6 |
|a Théorie des champs bayésienne.
|
| 650 |
|
7 |
|a SCIENCE
|x Physics
|x Mathematical & Computational.
|2 bisacsh
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| 650 |
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|a Bayesian field theory.
|2 fast
|0 (OCoLC)fst00829018
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| 776 |
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|i Print version:
|a Lemm, Jörg C.
|t Bayesian field theory.
|d Baltimore, Md. : Johns Hopkins University Press, 2003
|z 0801872200
|w (DLC) 2002073958
|w (OCoLC)50184931
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