logoPicV1 logoTextV1

Search Results

Below results based on the criteria 'Gibbs'
Total number of records returned: 9

Penalized Regression, Standard Errors, and Bayesian Lassos
Kyung, Minjung
Gill, Jeff
Ghosh, Malay
Casella, George

Uploaded 02-23-2010
Keywords model selection
Bayesian hierarchical models
LARS algorithm
EM/Gibbs sampler
Geometric Ergodicity
Gibbs Sampling
Abstract Penalized regression methods for simultaneous variable selection and coefficient estimation, especially those based on the lasso of Tibshirani (1996), have received a great deal of attention in recent years, mostly through frequentist models. Properties such as consistency have been studied, and are achieved by different lasso variations. Here we look at a fully Bayesian formulation of the problem, which is flexible enough to encompass most versions of the lasso that have been previously considered. The advantages of the hierarchical Bayesian formulations are many. In addition to the usual ease-of-interpretation of hierarchical models, the Bayesian formulation produces valid standard errors (which can be problematic for the frequentist lasso), and is based on a geometrically ergodic Markov chain. We compare the performance of the Bayesian lassos to their frequentist counterparts using simulations and data sets that previous lasso papers have used, and see that in terms of prediction mean squared error, the Bayesian lasso performance is similar to and, in some cases, better than, the frequentist lasso.

Parameterization and Bayesian Modeling
Gelman, Andrew

Uploaded 06-15-2004
Keywords censored data
data augmentation
Gibbs sampler
hierarchical model
missing data imputation
parameter expansion
prior distribution
truncated data
Abstract Progress in statistical computation often leads to advances in statistical modeling. For example, it is surprisingly common that an existing model is reparameterized, solely for computational purposes, but then this new configuration motivates a new family of models that is useful in applied statistics. One reason this phenomenon may not have been noticed in statistics is that reparameterizations do not change the likelihood. In a Bayesian framework, however, a transformation of parameters typically suggests a new family of prior distributions. We discuss examples in censored and truncated data, mixture modeling, multivariate imputation, stochastic processes, and multilevel models.

Estimating incumbency advantage and its variation, as an example of a before/after study
Gelman, Andrew
Huang, Zaiying

Uploaded 02-07-2003
Keywords Bayesian inference
before-after study
Congressional elections
Abstract Incumbency advantage is one of the most studied features in American legislative elections. In this paper, we construct and implement an estimate that allows incumbency advantage to vary between individual incumbents. This model predicts that open-seat elections will be less variable than those with incumbents running, an observed empirical pattern that is not explained by previous models. We apply our method to the U.S. House of Representatives in the twentieth century: our estimate of the overall pattern of incumbency advantage over time is similar to previous estimates (although slightly lower), and we also find a pattern of increasing variation. In addition to the application to incumbency advantage, our approach represents a new method, using multilevel modeling, for estimating effects in before/after studies.

Alternative Models of Dynamics in Binary Time-Series--Cross-Section Models: The Example of State Failure
Beck, Nathaniel
Jackman, Simon
Epstein, David
O'Halloran, Sharyn

Uploaded 07-14-2001
Keywords dynamic probit
state failure
Gibbs sampling
transitional models
discrete data
correlated binary data
generalized residuals
Abstract This paper investigates a variety of dynamic probit models for time-series--cross-section data in the context of explaining state failure. It shows that ordinary probit, which ignores dynamics, is misleading. Alternatives that seem to produce sensible results are the transition model and a model which includes a lagged emph{latent} dependent variable. It is argued that the use of a lagged latent variable is often superior to the use of a lagged realized dependent variable. It is also shown that the latter is a special case of the transition model. The relationship between the transition model and event history methods is also considered: the transition model estimates an event history model for both values of the dependent variable, yielding estimates that are identical to those produced by the two event history models. Furthermore, one can incorporate the insights gleaned from the event history models into the transition analysis, so that researchers do not have to assume duration independence. The conclusion notes that investigations of the various models have been limited to data sets which contain long sequences of zeros; models may perform differently in data sets with shorter bursts of zeros and ones.

Estimation Of Electoral Disproportionality And Thresholds Via MCMC
Kalandrakis, Anastassios

Uploaded 11-03-1999
Keywords Electoral Disproportionality
Electoral Thresholds
Gibbs Sampling
Metropolis Algorithm
Abstract For statistical as well as political reasons -- some already identified in the literature -- measures of both electoral disproportionality and electoral thresholds are essential and must be combined in numerical summaries of electoral institutions. With few exceptions, none of these quantities can be reliably inferred directly from the provisions of the electoral law, thus impairing "large scale" comparative studies. Through the use of sampling based Bayes methods I am able to simultaneously estimate these two quantities from electoral returns. I apply the proposed procedure on 45 electoral systems in use over 216 elections to the national parliaments in the 15 countries of the European Union in the period 1945-1996. The resultant two-dimensional summary of electoral systems has several attractive properties in comparison to indices of disproportionality currently used in comparative politics.

Senate Voting on NAFTA: The Power and Limitations of MCMC Methods for Studying Voting across Bills and across States
Smith, Alastair
McGillivray, Fiona

Uploaded 07-09-1996
Keywords NAFTA
Gibbs sampling
bivariate probit
Abstract We examine similarities in senate voting within states and across two senate bills: the 1991 fast track authorization bill and the 1993 NAFTA implementation bill. A series of bivariate probit models are estimated by Markov Chain Monte Carlo simulation. We discuss the power of MCMC techniques and how the output of these sampling procedures can be used for Bayesian model comparisons. Having separately explored the similarities in votes across bills and within states, we develop a 4-variate probit model to explain voting on NAFTA. The power of MCMC techniques to estimate this complicated model is demonstrated with two different MCMC procedures. We conclude by discussing the data requirements for these techniques.

A Bayesian Method for the Analysis of Dyadic Crisis Data
Smith, Alastair

Uploaded 11-04-1996
Keywords Bayesian model testing
Censored data
Crisis data
Gibbs sampling
Markov chain Monte Carlo
Ordered discrete choice model
Strategic choice
Abstract his paper examines the level of force that nations use during disputes. Suppose that two nations, A and B, are involved in a dispute. Each nation chooses the level of violence that it is prepared to use in order to achieve its objectives. Since there are two opponents making decisions, the outcome of the crisis is determined by a bivariate rather than univariate process. I propose a bivariate ordered discrete choice model to examine the relationship between nation A's decision to use force, nation B's decision to use force, and a series of explanatory variables. The model is estimated in the Bayesian context using a Markov chain Monte Carlo simulation technique. I analyze Bueno de Mesquita and Lalman's (1992) dyadically coded version of the Militarized Interstate Dispute data (Gochman and Moaz 1984). Various models are compared using Bayes Factors. The results indicate that nation A's and nation B's decisions to use force can not be regarded as independent. Bayesian model comparison show that variables derived from Bueno de Mesquita's expected utility theory (1982, 1985; Bueno de Mesquita and Lalman 1986, 1992) provide the best explanatory variables for decision making in crises.

The Spatial Probit Model of Interdependent Binary Outcomes: Estimation, Interpretation, and Presentation
Franzese, Robert
Hays, Jude

Uploaded 07-20-2007
Keywords Spatial Probit
Bayesian Gibbs-Sampler Estimator
Recursive Importance-Sampling Estimator
Abstract We have argued and shown elsewhere the ubiquity and prominence of spatial interdependence in political science research and noted that much previous practice has neglected this interdependence or treated it solely as nuisance to the serious detriment of sound inference. Previously, we considered only linear-regression models of spatial and/or spatio-temporal interdependence. In this paper, we turn to binary-outcome models. We start by stressing the ubiquity and centrality of interdependence in binary outcomes of interest to political and social scientists and note that, again, this interdependence has been ignored in most contexts where it likely arises and that, in the few contexts where it has been acknowledged, the endogeneity of the spatial lag has not be recognized. Next, we explain some of the severe challenges for empirical analysis posed by spatial interdependence in binary-outcome models, and then we follow recent advances in the spatial-econometric literature to suggest Bayesian or recursive-importance-sampling (RIS) approaches for tackling estimation. In brief and in general, the estimation complications arise because among the RHS variables is an endogenous weighted spatial-lag of the unobserved latent outcome, y*, in the other units; Bayesian or RIS techniques facilitate the complicated nested optimization exercise that follows from that fact. We also advance that literature by showing how to calculate estimated spatial effects (as opposed to parameter estimates) in such models, how to construct confidence regions for those (adopting a simulation strategy for the purpose), and how to present such estimates effectively.

Estimation in Dirichlet Random Effects Models
Kyung, Minjung
Gill, Jeff
Casella, George

Uploaded 04-28-2009
Keywords generalized linear mixed model
Dirichlet process random effects model
precision parameter likelihood
Gibbs sampling
importance sampling
probit mixed Dirichlet random effects model
Abstract We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distribution, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of the Dirichlet process, finding that maximum likelihood may not be desirable, but a posterior mode is a reasonable approach. Examples are given to show how these models perform on real data. Our results complement both the theoretical basis of the Dirichlet process nonparametric prior and the computational work that has been done to date. Forthcoming: Annals of Statistics.

< prev 1 next>