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30
Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction
, 2010
"... We use Lévy processes to generate joint prior distributions for a location parameter β = (β1,..., βp) as p grows large. This approach, which generalizes normal scalemixture priors to an infinitedimensional setting, has a number of connections with mathematical finance and Bayesian nonparametrics. ..."
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Cited by 16 (5 self)
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We use Lévy processes to generate joint prior distributions for a location parameter β = (β1,..., βp) as p grows large. This approach, which generalizes normal scalemixture priors to an infinitedimensional setting, has a number of connections with mathematical finance and Bayesian nonparametrics. We argue that it provides an intuitive framework for generating new regularization penalties and shrinkage rules; for performing asymptotic analysis on existing models; and for simplifying proofs of some classic results on normal scale mixtures.
A Bayesian Approach to Testing for Markov Switching in Univariate and Dynamic Factor Models
, 2000
"... Though Hamilton's (1989) Markov switching model has been widely estimated in various contexts, formal testing for Markov switching is not straightforward. Univariate tests in the classical framework by Hansen (1992) and Garcia (1998) do not reject the linear model for GDP. We present Bayesian tests ..."
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Cited by 15 (6 self)
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Though Hamilton's (1989) Markov switching model has been widely estimated in various contexts, formal testing for Markov switching is not straightforward. Univariate tests in the classical framework by Hansen (1992) and Garcia (1998) do not reject the linear model for GDP. We present Bayesian tests for Markov switching in both univariate and multivariate settings based on sensitivity of the posterior probability to the prior. We #nd that evidence for Markov switching, and thus the business cycle asymmetry, is stronger in a switching version of the dynamic factor model of Stock and Watson (1991) than it is for GDP by itself. Key Words: Bayesian Model Selection, Business Cycle Asymmetry, Dynamic Factor Model, Pseudo Prior, Model Indicator Parameter, Test of Markov Switching. JEL Classi#cations: C11, C12, E32. \The Bayesian moral is simple: Never make anything more than relative probability statements about the models explicitly entertained. Be suspicious of those who promise more!" [Po...
Diagnostic Measures for Model Criticism
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1996
"... ... In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear mo ..."
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Cited by 13 (1 self)
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... In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear models, and variable selection in regression and outlier detection. We illustrate our approach with two applications.
A simple Monte Carlo approach to Bayesian graduation
 Transactions of the Society of Actuaries
, 1992
"... The problem of graduating a sequence of data values can be cast as a statistical estimation problem. In particular, the Bayesian approach is attractive due to its ability to formally incorporate known ordering and smoothness conditions for the graduated values into the estimation structure. Howeve ..."
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Cited by 6 (0 self)
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The problem of graduating a sequence of data values can be cast as a statistical estimation problem. In particular, the Bayesian approach is attractive due to its ability to formally incorporate known ordering and smoothness conditions for the graduated values into the estimation structure. However, this approach has not been widely adopted in practice, primarily because of the arduousness of specifying the prior distributions for the graduated values and carrying out the necessary numerical integrations. This paper presents simple Bayesian graduation models that substantially ease the prior elicitation burden; it also describes a Monte Carlo integration approach that greatly reduces the computational load. The method is presented in generality and subsequently illustrated with two examples, one from the realm of health insurance and the other from the more traditional graduation context of mortality table construction. It is hoped that the method will stimulate greater use of the Bayesian paradigm within the actuarial community. 1.
Alternatives to the Gibbs Sampling Scheme
, 1992
"... A variation of the Gibbs sampling scheme is defined by driving the simulated Markov chain by the conditional distributions of an approximation to the posterior rather than the posterior distribution itself. Choosing a multivariate normal mixture form for the approximation enables reparametrization w ..."
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Cited by 6 (1 self)
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A variation of the Gibbs sampling scheme is defined by driving the simulated Markov chain by the conditional distributions of an approximation to the posterior rather than the posterior distribution itself. Choosing a multivariate normal mixture form for the approximation enables reparametrization which is crucial to improve convergence in the Gibbs sampler. Using an approximation to the posterior density also opens the possiblity to include a learning process about the  in the operational sense of evaluating posterior integrals  unknown posterior density in the algorithm. While ideally this should be done using available pointwise evaluations of the posterior density, this is too difficult in a general framework and we use instead the currently available Monte Carlo sample to adjust the approximating density. This is done using a simple multivariate implementation of the mixture of Dirichlet density estimation algorithm. Keywords: Markov chain Monte Carlo, Bayesian sampling, stocha...
Bayesian Computation and the Linear Model
, 2009
"... This paper is a review of computational strategies for Bayesian shrinkage and variable selection in the linear model. Our focus is less on traditional MCMC methods, which are covered in depth by earlier review papers. Instead, we focus more on recent innovations in stochastic search and adaptive MCM ..."
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Cited by 6 (0 self)
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This paper is a review of computational strategies for Bayesian shrinkage and variable selection in the linear model. Our focus is less on traditional MCMC methods, which are covered in depth by earlier review papers. Instead, we focus more on recent innovations in stochastic search and adaptive MCMC, along with some comparatively new research on shrinkage priors. One of our conclusions is that true MCMC seems inferior to stochastic search if one’s goal is to discover good models, but that stochastic search can result in biased estimates of variable inclusion probabilities. We also find reasons to question the accuracy of inclusion probabilities generated by traditional MCMC on highdimensional, nonorthogonal problems, though the matter is far from settled. Some key words: adaptive MCMC; linear models; shrinkage priors; stochastic search; variable selection 1
Learning About Heterogeneity in Returns to Schooling
, 2003
"... Using data from the National Longitudinal Survey of Youth (NLSY) we introduce and estimate various Bayesian hierarchical models that investigate the nature of unobserved heterogeneity in returns to schooling. We consider a variety of possible forms for the heterogeneity, some motivated by previou ..."
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Cited by 4 (1 self)
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Using data from the National Longitudinal Survey of Youth (NLSY) we introduce and estimate various Bayesian hierarchical models that investigate the nature of unobserved heterogeneity in returns to schooling. We consider a variety of possible forms for the heterogeneity, some motivated by previous theoretical and empirical work and some new ones, and let the data decide among the competing specifications. Empirical results indicate that heterogeneity is present in returns to education. Furthermore, we find strong evidence that the heterogeneity follows a continuous rather than discrete distribution, and that bivariate Normality provides a very reasonable description of individuallevel heterogeneity in intercepts and returns to schooling.
Conjugate Analysis of Multivariate Normal Data with Incomplete Observations
"... In this article we discuss families of prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. We present a general class of priors, modifying a proposal of Kadane and Trader, to allow incorporation of information about unidentified ..."
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Cited by 2 (0 self)
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In this article we discuss families of prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. We present a general class of priors, modifying a proposal of Kadane and Trader, to allow incorporation of information about unidentified parameters in the covariance matrix within a conjugate setting. We analyze the important special case of monotone patterns of missing data, providing an explicit recursive form for the posterior distribution resulting from a conjugate prior distribution. We derive the relationship between the prior and posterior hyperparameters in the Kadane and Trader formulation and the hyperparameters in the recursive factorization of the posterior distribution. We develop algorithms for sampling from the posterior distribution, that take advantage of the conjugate structure. In particular, the monotone case results can be exploited to handle the general case as well, thus providing ways of sampling from ...
Is There a Structural Break in the Equity Premium?
, 2000
"... In this paper, we apply a Bayesian approach to test for a structural break with unknown breakpoint in an empirical model of excess returns that allows the equity premium to change in response to recurrent changes in the level of volatility. The main questions we seek to answer with our approach are ..."
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Cited by 1 (0 self)
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In this paper, we apply a Bayesian approach to test for a structural break with unknown breakpoint in an empirical model of excess returns that allows the equity premium to change in response to recurrent changes in the level of volatility. The main questions we seek to answer with our approach are the following: Is there evidence of changes in the equity premium over time? If so, can these changes be explained as the consequence of recurrent changes in the level of volatility? Or, alternatively, does the equity premium undergo a onetime permanent structural break? For monthly excess returns on a valueweighted portfolio of NYSE stocks between 19261991, we find strong evidence for a structural break in the Markovswitching variance process around 1941. However, the data provide little evidence of a concurrent structural break in the equity premium. Instead, the data suggest that changes in the equity premium are mainly a consequence of recurrent changes in the level of volatility. Ke...
Conjugate Analysis of Multivariate Normal Data With Incomplete Observations
"... The authors discuss prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. They present a general class of priors for incorporating information about unidentified parameters in the covariance matrix. They analyze the special case of ..."
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The authors discuss prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. They present a general class of priors for incorporating information about unidentified parameters in the covariance matrix. They analyze the special case of monotone patterns of missing data, providing an explicit recursive form for the posterior distribution resulting from a conjugate prior distribution. They develop an importance sampling and a Gibbs sampling approach to sample from a general posterior distribution and compare the two methods. R ESUM E Les auteurs proposent des lois a priori conjuguees a la vraisemblance normale multivariee en presence d'observations incompletes. Ils decrivent une classe generale de lois a priori permettant d'incorporer de l'information concernant des parametres non identifies dans la matrice de covariance. Ils analysent le cas special oulepatrondesdonnees manquantes est monotone; ils montrent comment calcule...