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Below results based on the criteria 'Gibbs sampling'
Total number of records returned: 6

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.

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.

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.

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.

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