204,502 research outputs found
"Improved Empirical Bayes Ridge Regression Estimators under Multicollinearity"
No full textIn this paper we consider the problem of estimating the regression parameters in a multiple linear regression model when the multicollinearity is present.Under the assumption of normality, we present three empirical Bayes estimators. One of them shrinks the least squares (LS) estimator towards the principal component. The second one is a hierarchical empirical Bayes estimator shrinking the LS estimator twice.The third one is obtained by choosing di erent priors for the two sets of regression parameters that arise in the case of multicollinearity;this estimator is termed decomposed empirical Bayes estimator. These proposed estimators are not only proved to be uniformly better than the LS estimator, that is,minimax in terms of risk under the Strawderman's loss function,but also shown to be useful in the multicollinearity cases through simulation and empirical studies.
On a design consistency property of hierarchical Bayes estimators in finite population samplings.
No full textWe obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result suggests a simple way to correct the hierarchical Bayes estimator to achieve design-consistency, a well-known property in the traditional randomization approach to finite population sampling.We also suggest three different measures of uncertainty of our proposed estimator
Evaluation of elicitation methods to quantify Bayes linear models
No full textThe Bayes linear methodology allows decision makers to express their subjective beliefs and adjust these beliefs as observations are made. It is similar in spirit to probabilistic Bayesian approaches, but differs as it uses expectation as its primitive. While substantial work has been carried out in Bayes linear analysis, both in terms of theory development and application, there is little published material on the elicitation of structured expert judgement to quantify models. This paper investigates different methods that could be used by analysts when creating an elicitation process. The theoretical underpinnings of the elicitation methods developed are explored and an evaluation of their use is presented. This work was motivated by, and is a precursor to, an industrial application of Bayes linear modelling of the reliability of defence systems. An illustrative example demonstrates how the methods can be used in practice
Empirical Bayes methodology for estimating equipment failure rates with application to power generation plants
No full textMany reliability databases pool event data for equipment across different plants. Pooling may occur both within and between organizations with the intention of sharing data across common items within similar operating environments to provide better estimates of reliability and availability. Frequentist estimation methods can be poor when few, or no, events occur even when equipment operate for long periods. An alternative approach based upon empirical Bayes estimation is proposed. The new method is applied to failure data analysis in power generation plants and found to provide credible insights. A statistical comparison between the proposed and frequentist methods shows that empirical Bayes is capable of generating more accurate estimates
AN EMPIRICAL BAYES APPROACH TO MODELING DROUGHT
No full textThis paper illustrates an alternative approach to estimating the occurrence of drought. The empirical Bayes methodology was developed because of deficiencies in time-series and regression analysis with respect to prediction of drought. This manuscript is comprised of (a) a discussion of "classical" and Bayes estimators of probability density (or mass) functions, (b) a description of the model, and (c) a comparison of the performances of the empirical Bayes and two classical estimators in predicting the elapsed time until drought. The Bayes value (incorporating both a priori and data information) was found to be superior to the traditional estimates.Resource /Energy Economics and Policy,
Bayes linear kinematics in the analysis of failure rates and failure time distributions
No full textCollections of related Poisson or binomial counts arise, for example, from a number of different failures in similar machines or neighbouring time periods. A conventional Bayesian analysis requires a rather indirect prior specification and intensive numerical methods for posterior evaluations. An alternative approach using Bayes linear kinematics in which simple conjugate specifications for individual counts are linked through a Bayes linear belief structure is presented. Intensive numerical methods are not required. The use of transformations of the binomial and Poisson parameters is proposed. The approach is illustrated in two examples, one involving a Poisson count of failures, the other involving a binomial count in an analysis of failure times
Hierarchical Bayes prediction for the 2008 US Presidential election
No full textIn this paper a procedure is developed to derive the predictive density function of a future observation for prediction in a multiple regression model under hierarchical priors for the vector parameter. The derived predictive density function is applied for prediction in a multiple regression model given in Fair (2002) to study the effect of fluctuations in economic variables on voting behavior in U.S. presidential election. Numerical illustrations suggest that the predictive performance of Fair’s model is good under hierarchical Bayes setup, except for the 1992 election. Fair’s model under hierarchical Bayes setup indicates that the forthcoming 2008 US presidential election is likely to be a very close election slightly tilted towards Republicans. It is likely that republicans will get 50.90% vote with probability for win 0.550 in the 2008 US Presidential Election.
Merging expert and empirical data for rare event frequency estimation : pool homogenisation for empirical Bayes models
No full textEmpirical Bayes provides one approach to estimating the frequency of rare events as a weighted average of the frequencies of an event and a pool of events. The pool will draw upon, for example, events with similar precursors. The higher the degree of homogeneity of the pool, then the Empirical Bayes estimator will be more accurate. We propose and evaluate a new method using homogenisation factors under the assumption that events are generated from a Homogeneous Poisson Process. The homogenisation factors are scaling constants, which can be elicited through structured expert judgement and used to align the frequencies of different events, hence homogenising the pool. The estimation error relative to the homogeneity of the pool is examined theoretically indicating that reduced error is associated with larger pool homogeneity. The effects of misspecified expert assessments of the homogenisation factors are examined theoretically and through simulation experiments. Our results show that the proposed Empirical Bayes method using homogenisation factors is robust under different degrees of misspecification
A Decision tree-based attribute weighting filter for naive Bayes
No full textThe naive Bayes classifier continues to be a popular learning algorithm for data mining applications due to its simplicity and linear run-time. Many enhancements to the basic algorithm have been proposed to help mitigate its primary weakness--the assumption that attributes are independent given the class. All of them improve the performance of naïve Bayes at the expense (to a greater or lesser degree) of execution time and/or simplicity of the final model. In this paper we present a simple filter method for setting attribute weights for use with naive Bayes. Experimental results show that naive Bayes with attribute weights rarely degrades the quality of the model compared to standard naive Bayes and, in many cases, improves it dramatically. The main advantages of this method compared to other approaches for improving naive Bayes is its
run-time complexity and the fact that it maintains the simplicity of the final model
Bayes linear covariance matrix adjustment
No full textIn this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of random matrices is motivated and constructed. The inner-product on this space captures aspects of belief about the relationships between covariance matrices of interest, providing a structure rich enough to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability and related specifications to obtain representations allowing analysis. Adjustment is associated with orthogonal projection, and illustrated by examples for some common problems. The difficulties of adjusting the covariance matrices underlying exchangeable random vectors is tackled and discussed. Learning about the covariance matrices associated with multivariate time series dynamic linear models is shown to be amenable to a similar approach. Diagnostics for matrix adjustments are also discussed
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