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161
Bayesian Model Averaging for Linear Regression Models
 Journal of the American Statistical Association
, 1997
"... We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem in ..."
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Cited by 311 (15 self)
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We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem involves averaging over all possible models (i.e., combinations of predictors) when making inferences about quantities of
Predictive Model Selection
 Journal of the Royal Statistical Society, Ser. B
, 1995
"... this article we propose three criteria that can be used to address model selection. These emphasize observables rather than parameters and are based on a certain Bayesian predictive density. They have a unifying basis that is simple and interpretable,are free of asymptotic de#nitions,and allow the i ..."
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Cited by 97 (5 self)
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this article we propose three criteria that can be used to address model selection. These emphasize observables rather than parameters and are based on a certain Bayesian predictive density. They have a unifying basis that is simple and interpretable,are free of asymptotic de#nitions,and allow the incorporation of prior information. Moreover,two of these criteria are readily calibrated.
The variable selection problem
 Journal of the American Statistical Association
, 2000
"... The problem of variable selection is one of the most pervasive model selection problems in statistical applications. Often referred to as the problem of subset selection, it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables ..."
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Cited by 62 (3 self)
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The problem of variable selection is one of the most pervasive model selection problems in statistical applications. Often referred to as the problem of subset selection, it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors, but there is uncertainty about which subset to use. This vignette reviews some of the key developments which have led to the wide variety of approaches for this problem. 1
Model Selection and Accounting for Model Uncertainty in Linear Regression Models
, 1993
"... We consider the problems of variable selection and accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. The complete B ..."
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Cited by 52 (6 self)
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We consider the problems of variable selection and accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. The complete Bayesian solution to this problem involves averaging over all possible models when making inferences about quantities of interest. This approach is often not practical. In this paper we offer two alternative approaches. First we describe a Bayesian model selection algorithm called "Occam's "Window" which involves averaging over a reduced set of models. Second, we describe a Markov chain Monte Carlo approach which directly approximates the exact solution. Both these model averaging procedures provide better predictive performance than any single model which might reasonably have been selected. In the extreme case where there are many candidate predictors but there is no relationship between any of them and the response, standard variable selection procedures often choose some subset of variables that yields a high R² and a highly significant overall F value. We refer to this unfortunate phenomenon as "Freedman's Paradox" (Freedman, 1983). In this situation, Occam's vVindow usually indicates the null model as the only one to be considered, or else a small number of models including the null model, thus largely resolving the paradox.
Bayesian Model Averaging in proportional hazard models: Assessing the risk of a stroke
 Applied Statistics
, 1997
"... Evaluating the risk of stroke is important in reducing the incidence of this devastating disease. Here, we apply Bayesian model averaging to variable selection in Cox proportional hazard models in the context of the Cardiovascular Health Study, a comprehensive investigation into the risk factors for ..."
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Cited by 43 (5 self)
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Evaluating the risk of stroke is important in reducing the incidence of this devastating disease. Here, we apply Bayesian model averaging to variable selection in Cox proportional hazard models in the context of the Cardiovascular Health Study, a comprehensive investigation into the risk factors for stroke. We introduce a technique based on the leaps and bounds algorithm which e ciently locates and ts the best models in the very large model space and thereby extends all subsets regression to Cox models. For each independent variable considered, the method provides the posterior probability that it belongs in the model. This is more directly interpretable than the corresponding Pvalues, and also more valid in that it takes account of model uncertainty. Pvalues from models preferred by stepwise methods tend to overstate the evidence for the predictive value of a variable. In our data Bayesian model averaging predictively outperforms standard model selection methods for assessing
Shotgun stochastic search for “large p” regression
 Journal of the American Statistical Association
, 2007
"... Model search in regression with very large numbers of candidate predictors raises challenges for both model specification and computation, and standard approaches such as Markov chain Monte Carlo (MCMC) and stepwise methods are often infeasible or ineffective. We describe a novel shotgun stochastic ..."
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Cited by 36 (3 self)
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Model search in regression with very large numbers of candidate predictors raises challenges for both model specification and computation, and standard approaches such as Markov chain Monte Carlo (MCMC) and stepwise methods are often infeasible or ineffective. We describe a novel shotgun stochastic search (SSS) approach that explores “interesting” regions of the resulting, very highdimensional model spaces to quickly identify regions of high posterior probability over models. We describe algorithmic and modeling aspects, priors over the model space that induce sparsity and parsimony over and above the traditional dimension penalization implicit in Bayesian and likelihood analyses, and parallel computation using cluster computers. We discuss an example from gene expression cancer genomics, comparisons with MCMC and other methods, and theoretical and simulationbased aspects of performance characteristics in largescale regression model search. We also provide software implementing the methods.
Principal component estimation of functional logistic regression: discussion of two different approaches
 Journal of Nonparametric Statistics
, 2004
"... Over the last few years many methods have been developed for analyzing functional data with different objectives. The purpose of this paper is to predict a binary response variable in terms of a functional variable whose sample information is given by a set of curves measured without error. In order ..."
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Cited by 26 (2 self)
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Over the last few years many methods have been developed for analyzing functional data with different objectives. The purpose of this paper is to predict a binary response variable in terms of a functional variable whose sample information is given by a set of curves measured without error. In order to solve this problem we formulate a functional logistic regression model and propose its estimation by approximating the sample paths in a finite dimensional space generated by a basis. Then, the problem is reduced to a multiple logistic regression model with highly correlated covariates. In order to reduce dimension and to avoid multicollinearity, two different approaches of functional principal component analysis of the sample paths are proposed. Finally, a simulation study for evaluating the estimating performance of the proposed principal component approaches is developed.
Discounts on illiquid stocks: Evidence from China, Yale School of Management working paper
, 2001
"... This paper provides evidence on the significant impact of illiquidity or nonmarketability on security valuation. A typical listed company in China has several types of share outstanding: (i) common shares that are only tradable on stock exchanges, (ii) restricted institutional shares (RIS) that are ..."
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Cited by 25 (3 self)
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This paper provides evidence on the significant impact of illiquidity or nonmarketability on security valuation. A typical listed company in China has several types of share outstanding: (i) common shares that are only tradable on stock exchanges, (ii) restricted institutional shares (RIS) that are not tradable and can only be transferred privately or through irregularly scheduled auctions, and (iii) state shares that are only transferable privately. These types of share are identical in every aspect, except that market regulations make state and RIS shares almost totally illiquid. Our analysis focuses on the price differences between RIS and common shares of the same company, using both auction and privatetransfer transactions for RIS shares. Among our findings, the average discount for RIS shares relative to their floating counterpart is 77.93 % and 85.59%, respectively based on auction and private transfers. The price for illiquidity is thus high, significantly raising the cost of equity capital. This illiquidity discount increases with both the floating shares ’ volatility and the firm’s debt/equity ratio, but decreases with firm size, return on equity, and book/price and earnings/price ratios (based on the floating
Sigmoid relationships between nutrients and chlorophyll among lakes
, 1989
"... Previous studies of freshwater eutrophication have shown that algal biomass tends to increase with the supply of dissolved phosphorus. This concept has been condensed into empirical relationships between chlorophyll a and total phosphorus concentrations (convenient measures of algal biomass and phos ..."
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Cited by 25 (1 self)
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Previous studies of freshwater eutrophication have shown that algal biomass tends to increase with the supply of dissolved phosphorus. This concept has been condensed into empirical relationships between chlorophyll a and total phosphorus concentrations (convenient measures of algal biomass and phosphorus availability) which have become essential tools in theoretical and applied limnology. With few exceptions, ecologists accept the idea that chlorophyll concentration rises linearly with phosphorus concentration among lakes. Such a suggestion runs counter to Liebigian principles of fertilization however, and contradicts laboratory and field research indicating the influence of other nutrients. Our analysis of two large independent phosphoruschlorophyll data sets from temperatezone lakes shows that log phosphoruslog chlorophyll relationships are sigmoid in shape and that a second nutrient, nitrogen, has a significant impact on chlorophyll concentrations when phosphorus availability is high. Our new empirical relationships indicate that mechanisms regulating algal biomass change with enrich ment, and suggest new management strategies for polluted lakes. Les r&ultats d'&udes ante>ieures sur I'eutrophisation des eaux douces montrent que la biomasse algale a tendance a augmenter avec I'accumulation de phosphore dissous. On a exprim £ ce concept par des rapports empiriques entre la chlorophylle a et les concentrations de phosphore total (mesures pratiques de la biomasse algale et de la quantity de phosphore disponible), qui sont devenus des outils essentiels en limnologie the'orique et appliqu£e.