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Author

Gideon Schwarz

Bio: Gideon Schwarz is an academic researcher. The author has contributed to research in topic(s): Asymptotic expansion & Bayes' theorem. The author has an hindex of 3, co-authored 3 publication(s) receiving 69467 citation(s).

Papers
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Journal ArticleDOI
TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
Abstract: The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.

35,659 citations

01 Jan 2005
TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
Abstract: The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.

33,801 citations

Journal ArticleDOI
TL;DR: In this paper, Fortus' generalization of asymptotic shapes of optimal testing regions for composite hypotheses does away with the restriction to exponential families originally imposed by us, and suggests some improvements that may be crucial for its practical applicability to parametric problems, and point out its shortcomings for nonparametric ones.
Abstract: : Fortus' generalization (1979) of asymptotic shapes of optimal testing regions for composite hypotheses does away with the restriction to exponential families originally imposed by us (1962). Here we survey his work critically, and suggest some improvements that may be crucial for its practical applicability to parametric problems, and point out its shortcomings for nonparametric ones. (Author)

7 citations


Cited by
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Book
Vladimir Vapnik1
01 Jan 1995
TL;DR: Setting of the learning problem consistency of learning processes bounds on the rate of convergence ofLearning processes controlling the generalization ability of learning process constructing learning algorithms what is important in learning theory?
Abstract: Setting of the learning problem consistency of learning processes bounds on the rate of convergence of learning processes controlling the generalization ability of learning processes constructing learning algorithms what is important in learning theory?.

38,164 citations

Journal ArticleDOI
TL;DR: The newest addition in MEGA5 is a collection of maximum likelihood (ML) analyses for inferring evolutionary trees, selecting best-fit substitution models, inferring ancestral states and sequences, and estimating evolutionary rates site-by-site.
Abstract: Comparative analysis of molecular sequence data is essential for reconstructing the evolutionary histories of species and inferring the nature and extent of selective forces shaping the evolution of genes and species. Here, we announce the release of Molecular Evolutionary Genetics Analysis version 5 (MEGA5), which is a user-friendly software for mining online databases, building sequence alignments and phylogenetic trees, and using methods of evolutionary bioinformatics in basic biology, biomedicine, and evolution. The newest addition in MEGA5 is a collection of maximum likelihood (ML) analyses for inferring evolutionary trees, selecting best-fit substitution models (nucleotide or amino acid), inferring ancestral states and sequences (along with probabilities), and estimating evolutionary rates site-by-site. In computer simulation analyses, ML tree inference algorithms in MEGA5 compared favorably with other software packages in terms of computational efficiency and the accuracy of the estimates of phylogenetic trees, substitution parameters, and rate variation among sites. The MEGA user interface has now been enhanced to be activity driven to make it easier for the use of both beginners and experienced scientists. This version of MEGA is intended for the Windows platform, and it has been configured for effective use on Mac OS X and Linux desktops. It is available free of charge from http://www.megasoftware.net.

37,583 citations

Journal ArticleDOI
TL;DR: In this article, structural equation models with latent variables are defined, critiqued, and illustrated, and an overall program for model evaluation is proposed based upon an interpretation of converging and diverging evidence.
Abstract: Criteria for evaluating structural equation models with latent variables are defined, critiqued, and illustrated. An overall program for model evaluation is proposed based upon an interpretation of converging and diverging evidence. Model assessment is considered to be a complex process mixing statistical criteria with philosophical, historical, and theoretical elements. Inevitably the process entails some attempt at a reconcilation between so-called objective and subjective norms.

17,246 citations

Journal ArticleDOI
TL;DR: jModelTest 2: more models, new heuristics and parallel computing Diego Darriba, Guillermo L. Taboada, Ramón Doallo and David Posada.
Abstract: jModelTest 2: more models, new heuristics and parallel computing Diego Darriba, Guillermo L. Taboada, Ramón Doallo and David Posada Supplementary Table 1. New features in jModelTest 2 Supplementary Table 2. Model selection accuracy Supplementary Table 3. Mean square errors for model averaged estimates Supplementary Note 1. Hill-climbing hierarchical clustering algorithm Supplementary Note 2. Heuristic filtering Supplementary Note 3. Simulations from prior distributions Supplementary Note 4. Speed-up benchmark on real and simulated datasets

10,986 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined and derive a measure pD for the effective number in a model as the difference between the posterior mean of the deviances and the deviance at the posterior means of the parameters of interest, which is related to other information criteria and has an approximate decision theoretic justification.
Abstract: Summary. We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure pD for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general pD approximately corresponds to the trace of the product of Fisher's information and the posterior covariance, which in normal models is the trace of the ‘hat’ matrix projecting observations onto fitted values. Its properties in exponential families are explored. The posterior mean deviance is suggested as a Bayesian measure of fit or adequacy, and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. Adding pD to the posterior mean deviance gives a deviance information criterion for comparing models, which is related to other information criteria and has an approximate decision theoretic justification. The procedure is illustrated in some examples, and comparisons are drawn with alternative Bayesian and classical proposals. Throughout it is emphasized that the quantities required are trivial to compute in a Markov chain Monte Carlo analysis.

10,825 citations