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177
An exact likelihood analysis of the multinomial probit model
, 1994
"... We develop new methods for conducting a finite sample, likelihoodbased analysis of the multinomial probit model. Using a variant of the Gibbs sampler, an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors. This approach avoids direct evalu ..."
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Cited by 117 (5 self)
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We develop new methods for conducting a finite sample, likelihoodbased analysis of the multinomial probit model. Using a variant of the Gibbs sampler, an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors. This approach avoids direct evaluation of the likelihood and, thus, avoids the problems associated with calculating choice probabilities which affect both the standard likelihood and method of simulated moments approaches. Both simulated and actual consumer panel data are used to fit sixdimensional choice models. We also develop methods for analyzing random coefficient and multiperiod probit models.
Inference in longhorizon event studies: A bayesian approach with an application to initial public offerings
 Journal of Finance
, 2000
"... Statistical inference in longhorizon event studies has been hampered by the fact that abnormal returns are neither normally distributed nor independent. This study presents a new approach to inference that overcomes these difficulties and dominates other popular testing methods. I illustrate the us ..."
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Cited by 53 (3 self)
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Statistical inference in longhorizon event studies has been hampered by the fact that abnormal returns are neither normally distributed nor independent. This study presents a new approach to inference that overcomes these difficulties and dominates other popular testing methods. I illustrate the use of the methodology by examining the longhorizon returns of initial public offerings ~IPOs!. I find that the Fama and French ~1993! threefactor model is inconsistent with the observed longhorizon price performance of these IPOs, whereas a characteristicbased model cannot be rejected. RECENT EMPIRICAL STUDIES IN FINANCE document systematic longrun abnormal price reactions subsequent to numerous corporate activities. 1 Since these results imply that stock prices react with a long delay to publicly available information, they appear to be at odds with the Efficient Markets Hypothesis ~EMH!. Longrun event studies, however, are subject to serious statistical difficulties
Modeling Multilevel Data Structures
 AMERICAN JOURNAL OF POLITICAL SCIENCE
, 1997
"... Although integrating multiple levels of data into an analysis can often yield better inferences about the phenomenon under study, traditional methodologies used to combine multiple levels of data are problematic. In this paper, we discuss several methodologies under the rubric of multilevel analys ..."
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Cited by 52 (0 self)
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Although integrating multiple levels of data into an analysis can often yield better inferences about the phenomenon under study, traditional methodologies used to combine multiple levels of data are problematic. In this paper, we discuss several methodologies under the rubric of multilevel analysis. Multilevel methods, we argue, provide researchers, particularly researchers using comparative data, substantial leverage in overcoming the typical problems associated with either ignoring multiple levels of data, or problems associated with combining lowerlevel and higherlevel data (including overcoming implicit assumptions of fixed and constant effects). The paper discusses several variants of the multilevel model and provides an application of individuallevel support for European integration using comparative political data from Western Europe.
Bayesian estimation of a multilevel IRT model using Gibbs sampling
 Psychometrika
, 2001
"... In this article, atwolevel regression model is imposed on the ability parameters in an item response theory (IRT) model. The advantage of using latent rather an observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficu ..."
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Cited by 36 (6 self)
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In this article, atwolevel regression model is imposed on the ability parameters in an item response theory (IRT) model. The advantage of using latent rather an observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement rror. Another advantage is that, contrary to observed scores, latent scores are testindependent, which offers the possibility of using results from different tests in one analysis where the parameters of the IRT model and the multilevel model can be concurrently estimated. The twoparameter no mal ogive model is used for the IRT measurement model. It will be shown that he parameters of the twoparameter normal ogive model and the multilevel model can be estimated in a Bayesian framework using Gibbs sampling. Examples using simulated and real data are given.
Modeling individual differences using Dirichlet processes
, 2006
"... We introduce a Bayesian framework for modeling individual differences, in which subjects are assumed to belong to one of a potentially infinite number of groups. In this model, the groups observed in any particular data set are not viewed as a fixed set that fully explains the variation between indi ..."
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Cited by 30 (13 self)
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We introduce a Bayesian framework for modeling individual differences, in which subjects are assumed to belong to one of a potentially infinite number of groups. In this model, the groups observed in any particular data set are not viewed as a fixed set that fully explains the variation between individuals, but rather as representatives of a latent, arbitrarily rich structure. As more people are seen, and more details about the individual differences are revealed, the number of inferred groups is allowed to grow. We use the Dirichlet process—a distribution widely used in nonparametric Bayesian statistics—to define a prior for the model, allowing us to learn flexible parameter distributions without overfitting the data, or requiring the complex computations typically required for determining the dimensionality of a model. As an initial demonstration of the approach, we present three applications that analyze the individual differences in category learning, choice of publication outlets, and webbrowsing behavior.
Bayesian robust inference for differential gene expression in microarrays with multiple samples
 Biometrics
"... We consider the problem of identifying differentially expressed genes under different conditions using gene expression microarrays. Because of the many steps involved in the experimental process, from hybridization to image analysis, cDNA microarray data often contain outliers. For example, an outly ..."
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Cited by 27 (6 self)
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We consider the problem of identifying differentially expressed genes under different conditions using gene expression microarrays. Because of the many steps involved in the experimental process, from hybridization to image analysis, cDNA microarray data often contain outliers. For example, an outlying data value could occur because of scratches or dust on the surface, imperfections in the glass, or imperfections in the array production. We develop a robust Bayesian hierarchical model for testing for differential expression. Errors are modeled explicitly using a tdistribution, which accounts for outliers. The model includes an exchangeable prior for the variances which allow different variances for the genes but still shrink extreme empirical variances. Our model can be used for testing for differentially expressed genes among multiple samples, and it can distinguish between the different possible patterns of differential expression when there are three or more samples. Parameter estimation is carried out using a novel version of Markov chain Monte Carlo that is appropriate when the model puts mass on subspaces of the full parameter space. The method is illustrated using two publicly available gene expression data sets. We compare our method to six other baseline and commonly used techniques, namely the ttest, the Bonferroniadjusted ttest, Significance Analysis of Microarrays (SAM), Efron’s empirical Bayes, and EBarrays in both its LognormalNormal and GammaGamma forms. In an experiment with HIV data, our method performed better than these alternatives, on the basis of betweenreplicate agreement and disagreement.
Gaussian regression and optimal finite dimensional linear models
 In C. M. Bishop (Ed.)., Neural
, 1998
"... The problem of regression under Gaussian assumptions is treated generally. The relationship between Bayesian prediction, regularization and smoothing is elucidated. The ideal regression is the posterior mean and its computation scales asO(n3), wherenis the sample size. We show that the optimalmdime ..."
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Cited by 22 (5 self)
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The problem of regression under Gaussian assumptions is treated generally. The relationship between Bayesian prediction, regularization and smoothing is elucidated. The ideal regression is the posterior mean and its computation scales asO(n3), wherenis the sample size. We show that the optimalmdimensional linear model under a given prior is spanned by the firstmeigenfunctions of a covariance operator, which is a traceclass operator. This is an infinite dimensional analogue of principal component analysis. The importance of Hilbert space methods to practical statistics is also discussed.
Bayesian Tests And Model Diagnostics In Conditionally Independent Hierarchical Models
 Journal of the American Statistical Association
, 1994
"... Consider the conditionally independent hierarchical model (CIHM) where observations y i are independently distributed from f(y i j` i ), the parameters ` i are independently distributed from distributions g(`j), and the hyperparameters are distributed according to a distribution h(). The posterior ..."
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Cited by 19 (1 self)
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Consider the conditionally independent hierarchical model (CIHM) where observations y i are independently distributed from f(y i j` i ), the parameters ` i are independently distributed from distributions g(`j), and the hyperparameters are distributed according to a distribution h(). The posterior distribution of all parameters of the CIHM can be efficiently simulated by Monte Carlo Markov Chain (MCMC) algorithms. Although these simulation algorithms have facilitated the application of CIHM's, they generally have not addressed the problem of computing quantities useful in model selection. This paper explores how MCMC simulation algorithms and other related computational algorithms can be used to compute Bayes factors that are useful in criticizing a particular CIHM. In the case where the CIHM models a belief that the parameters are exchangeable or lie on a regression surface, the Bayes factor can measure the consistency of the data with the structural prior belief. Bayes factors can ...
Bayesian forecasting of an inhomogeneous Poisson process with applications to call center data. To appear
 Journal of the American Statistical Association
, 2007
"... A call center is a centralized hub where customer and other telephone calls are dealt with by an organization. In today’s economy, they have become the primary point of contact between customers and businesses. Accurate prediction of the call arrival rate is therefore indispensable for call center ..."
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Cited by 18 (2 self)
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A call center is a centralized hub where customer and other telephone calls are dealt with by an organization. In today’s economy, they have become the primary point of contact between customers and businesses. Accurate prediction of the call arrival rate is therefore indispensable for call center practitioners to staff their call center efficiently and cost effectively. This article proposes a multiplicative model for modeling and forecasting withinday arrival rates to a US commercial bank’s call center. Markov chain Monte Carlo sampling methods are used to estimate both latent states and model parameters. Onedayahead density forecasts for the rates and counts are provided. The calibration of these predictive distributions is evaluated through probability integral transforms. Furthermore, we provide onedayahead forecasts comparisons with classical statistical models. Our predictions show significant improvements of up to 25 % over these standards. A sequential Monte Carlo algorithm is also proposed for sequential estimation and forecasts of the model parameters and rates.
A Bayesian formulation of exploratory data analysis and goodnessoffit testing
, 2003
"... Exploratory data analysis (EDA) and Bayesian inference (or, more generally, complex statistical modeling)which are generally considered as unrelated statistical paradigmscan be particularly eective in combination. In this paper, we present a Bayesian framework for EDA based on posterior predict ..."
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Cited by 17 (8 self)
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Exploratory data analysis (EDA) and Bayesian inference (or, more generally, complex statistical modeling)which are generally considered as unrelated statistical paradigmscan be particularly eective in combination. In this paper, we present a Bayesian framework for EDA based on posterior predictive checks. We explain how posterior predictive simulations can be used to create reference distributions for EDA graphs, and how this approach resolves some theoretical problems in Bayesian data analysis. We show how the generalization of Bayesian inference to include replicated data y and replicated parameters follows a long tradition of generalizations in Bayesian theory.