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Author : Giuseppe De Luca
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (838 download)
Download or read book Bayesian Model Averaging and Weighted Average Least Squares written by Giuseppe De Luca and published by . This book was released on 2011 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J.R Magnus
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Weighted-Average Least Squares (WALS) written by J.R Magnus and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model averaging has become a popular method of estimation, following increasing evidence that model selection and estimation should be treated as one joint procedure. Weighted-average least squares (WALS) is a recent model-average approach, which takes an intermediate position between frequentist and Bayesian methods, allows a credible treatment of ignorance, and is extremely fast to compute. We review the theory of WALS and discuss extensions and applications.
Author : Giuseppe De Luca
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (13 download)
Download or read book Weighted-Average Least Squares Estimation of Generalized Linear Models written by Giuseppe De Luca and published by . This book was released on 2017 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: The weighted-average least squares (WALS) approach, introduced by Magnus et al. (2010) in the context of Gaussian linear models, has been shown to enjoy important advantages over other strictly Bayesian and strictly frequentist model averaging estimators when accounting for problems of uncertainty in the choice of the regressors. In this paper we extend the WALS approach to deal with uncertainty about the specification of the linear predictor in the wider class of generalized linear models (GLMs). We study the large-sample properties of the WALS estimator for GLMs under a local misspecification framework that allows the development of asymptotic model averaging theory. We also investigate the finite sample properties of this estimator by a Monte Carlo experiment whose design is based on the real empirical analysis of attrition in the first two waves of the Survey of Health, Ageing and Retirement in Europe (SHARE).
Author : J.R Magnus
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Concept-Based Bayesian Model Averaging and Growth Empirics written by J.R Magnus and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In specifying a regression equation, we need to determine which regressors to include, but also how these regressors are measured. This gives rise to two levels of uncertainty: concepts (level 1) and measurements within each concept (level 2). In this paper we propose a hierarchical weighted least squares (HWALS) method to address these uncertainties. We examine the effects of different growth theories taking into account the measurement problem in the growth regression. We find that estimates produced by HWALS provide intuitive and robust explanations. We also consider approximation techniques when the number of variables is large or when computing time is limited, and we propose possible strategies for sensitivity analysis.
Author : Jan Rudolf Magnus
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (228 download)
Download or read book A Comparison of Two Averaging Techniques with an Application to Growth Empirics written by Jan Rudolf Magnus and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dong Dai
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.:/5 (87 download)
Download or read book Bayesian Model Averaging with Exponentiated Least Square Loss written by Dong Dai and published by . This book was released on 2013 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a finite family of functions, the goal of model averaging is to construct a procedure that mimics the function from this family that is the closest to an unknown regression function. More precisely, we consider a general regression model with fi xed design and measure the distance between functions by mean squared error (MSE) at the design points. In this thesis, we propose a new method Bayesian model averaging with exponentiated least square loss (BMAX) to solve the model averaging problem optimally in a minimax sense.
Author : Giuseppe De Luca
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (131 download)
Download or read book Asymptotic Properties of the Weighted-average Least Squares (WALS) Estimator written by Giuseppe De Luca and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate the asymptotic behavior of the WALS estimator, a model-averaging estimator with attractive finite-sample and computational properties. WALS is closely related to the normal location model, and hence much of the paper concerns the asymptotic behavior of the estimator of the unknown mean in the normal local model. Since we adopt a frequentist-Bayesian approach, this specializes to the asymptotic behavior of the posterior mean as a frequentist estimator of the normal location parameter. We emphasize two challenging issues. First, our definition of ignorance in the Bayesian step involves a prior on the t-ratio rather than on the parameter itself. Second, instead of assuming a local misspecification framework, we consider a standard asymptotic setup with fixed parameters. We show that, under suitable conditions on the prior, the WALS estimator is √n-consistent and its asymptotic distribution essentially coincides with that of the unrestricted least-squares estimator. Monte Carlo simulations confirm our theoretical results.
Author : James P. LeSage
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Bayesian Model Averaging for Spatial Econometric Models written by James P. LeSage and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We extend the literature on Bayesian model comparison for ordinary least-squares regression models to include spatial autoregressive and spatial error models. Our focus is on comparing models that consist of different matrices of explanatory variables. A Markov Chain Monte Carlo model composition methodology labelled MC to the third by Madigan and York (1995) is developed for two types of spatial econometric models that are frequently used in the literature. The methodology deals with cases where the number of possible models based on different combinations of candidate explanatory variables is large enough that calculation of posterior probabilities for all models is difficult or infeasible. Estimates and inferences are produced by averaging over models using the posterior model probabilities as weights, a procedure known as Bayesian model averaging. We illustrate the methods using a spatial econometric model of origin-destination population migration flows between the 48 US States and District of Columbia during the 1990 to 2000 period.
Author : Jiayin Zheng
Publisher :
ISBN 13 :
Total Pages : 150 pages
Book Rating : 4.:/5 (18 download)
Download or read book Calibrated Bayes Factor and Bayesian Model Averaging written by Jiayin Zheng and published by . This book was released on 2018 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a rich history of work on model selection and averaging in the statistics literature. The Bayesian paradigm provides an approach to model selection which successfully overcomes the drawbacks for which frequentist hypothesis testing has been criticized. Most commonly, Bayesian model selection methods are based on the Bayes factor. Additionally, the Bayes factor has applications outside the realm of model selection, such as model averaging. In a formal sense, as a supplement to the prior odds, the Bayes factor produces the posterior odds for a pair of models. These posterior odds can be translated to posterior probabilities and yields a full posterior distribution that assigns a probability to each model as well as a distribution over the parameters for each model. Then the Bayesian model averaging provides better prediction by making inferences based on a weighted average over all of the models considered.
Author : Tian Xie
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (11 download)
Download or read book Least Squares Model Averaging by Prediction Criterion written by Tian Xie and published by . This book was released on 2012 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Zhen Wang
Publisher :
ISBN 13 :
Total Pages : 107 pages
Book Rating : 4.:/5 (611 download)
Download or read book Semi-parametric Bayesian Models Extending Weighted Least Squares written by Zhen Wang and published by . This book was released on 2009 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Weighted least squares regression is tied to normality of the residual distribution. The two main motivations for weights are scale families and convolution families. In normal-theory regression, normality is retained under both scaling and convolution. Outside of normal-theory regression, the two motivations lead to different models and inferences. Under a scale model, the shape of the residual distribution remains the same; under a convolution model, the distribution moves toward normality as more units are convolved. Empirically, we have observed both the scale family and the convolution family. Some data sets show slower movement toward normality than convolution would suggest.
Author : Giuseppe De Luca
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (118 download)
Download or read book Sampling Properties of the Bayesian Posterior Mean with an Application to WALS Estimation written by Giuseppe De Luca and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein-von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this paper we explore this issue by first considering the frequentist properties (bias and variance) of the posterior mean in the important case of the normal location model, which consists of a single observation on a univariate Gaussian distribution with unknown mean and known variance. Based on these results, we derive new estimators of the frequentist bias and variance of the WALS estimator in finite samples. We then study the finite-sample performance of the proposed estimators by a Monte Carlo experiment with design derived from a real data application about the effect of abortion on crime rates.
Author : David Fletcher
Publisher : Springer
ISBN 13 : 3662585413
Total Pages : 107 pages
Book Rating : 4.6/5 (625 download)
Download or read book Model Averaging written by David Fletcher and published by Springer. This book was released on 2019-01-17 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise and accessible overview of model averaging, with a focus on applications. Model averaging is a common means of allowing for model uncertainty when analysing data, and has been used in a wide range of application areas, such as ecology, econometrics, meteorology and pharmacology. The book presents an overview of the methods developed in this area, illustrating many of them with examples from the life sciences involving real-world data. It also includes an extensive list of references and suggestions for further research. Further, it clearly demonstrates the links between the methods developed in statistics, econometrics and machine learning, as well as the connection between the Bayesian and frequentist approaches to model averaging. The book appeals to statisticians and scientists interested in what methods are available, how they differ and what is known about their properties. It is assumed that readers are familiar with the basic concepts of statistical theory and modelling, including probability, likelihood and generalized linear models.
Author : Paul Damien
Publisher : Oxford University Press
ISBN 13 : 0199695601
Total Pages : 717 pages
Book Rating : 4.1/5 (996 download)
Download or read book Bayesian Theory and Applications written by Paul Damien and published by Oxford University Press. This book was released on 2013-01-24 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field.
Author : Eduardo Ley
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (318 download)
Download or read book On the Effect of Prior Assumptions in Bayesian Model Averaging with Applications to Growth Regression written by Eduardo Ley and published by . This book was released on 2007 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines the problem of variable selection in linear regression models. Bayesian model averaging has become an important tool in empirical settings with large numbers of potential regressors and relatively limited numbers of observations. The paper analyzes the effect of a variety of prior assumptions on the inference concerning model size, posterior inclusion probabilities of regressors, and predictive performance. The analysis illustrates these issues in the context of cross-country growth regressions using three datasets with 41 to 67 potential drivers of growth and 72 to 93 observations. The results favor particular prior structures for use in this and related contexts.
Author : Andrew Gelman
Publisher : CRC Press
ISBN 13 : 1439840954
Total Pages : 677 pages
Book Rating : 4.4/5 (398 download)
Download or read book Bayesian Data Analysis, Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Author : P. Cheeseman
Publisher : Springer Science & Business Media
ISBN 13 : 1461226600
Total Pages : 475 pages
Book Rating : 4.4/5 (612 download)
Download or read book Selecting Models from Data written by P. Cheeseman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a selection of papers presented at the Fourth International Workshop on Artificial Intelligence and Statistics held in January 1993. These biennial workshops have succeeded in bringing together researchers from Artificial Intelligence and from Statistics to discuss problems of mutual interest. The exchange has broadened research in both fields and has strongly encour aged interdisciplinary work. The theme ofthe 1993 AI and Statistics workshop was: "Selecting Models from Data". The papers in this volume attest to the diversity of approaches to model selection and to the ubiquity of the problem. Both statistics and artificial intelligence have independently developed approaches to model selection and the corresponding algorithms to implement them. But as these papers make clear, there is a high degree of overlap between the different approaches. In particular, there is agreement that the fundamental problem is the avoidence of "overfitting"-Le., where a model fits the given data very closely, but is a poor predictor for new data; in other words, the model has partly fitted the "noise" in the original data.
