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Simulating Normalized Constants: From Importance Sampling to Bridge Sampling to Path Sampling
 Statistical Science, 13, 163–185. COMPARISON OF METHODS FOR COMPUTING BAYES FACTORS 435
, 1998
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Cited by 146 (4 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Estimating the probability of events that have never occurred: when is your vote decisive
 Journal of the American Statistical Association
, 1998
"... Researchers sometimes argue that statisticians have little to contribute when few realizations of the process being estimated are observed. We show that this argument is incorrect even in the extreme situation of estimating the probabilities of events so rare that they have never occurred. We show h ..."
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Cited by 29 (14 self)
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Researchers sometimes argue that statisticians have little to contribute when few realizations of the process being estimated are observed. We show that this argument is incorrect even in the extreme situation of estimating the probabilities of events so rare that they have never occurred. We show how statistical forecasting models allow us to use empirical data to improve inferences about the probabilities of these events. Our application is estimating the probability that your vote will be decisive in a U.S. presidential election, a problem that has been studied by political scientists for more than two decades. The exact value of this probability is of only minor interest, but the number has important implications for understanding the optimal allocation of campaign resources, whether states and voter groups receive their fair share of attention from prospective presidents, and how formal "rational choice" models of voter behavior might be able to explain why people vote at all. We show how the probability of a decisive vote can be estimated empirically from statelevel forecasts of the presidential election and illustrate with the example of 1992. Based on generalizations of standard political science forecasting models, we estimate the (prospective) probability of a single vote being decisive as about 1 in 10 million for close national elections such as 1992, varying by about a factor of 10 among states. Our results support the argument that subjective probabilities of many types are best obtained through empirically based statistical prediction models rather than solely through mathematical reasoning. We discuss the implications of our findings for the types of decision analyses used in public choice studies.
Transformed and parameterexpanded Gibbs samplers for multilevel linear and generalized linear models
, 2004
"... Hierarchical linear and generalized linear models can be fit using Gibbs samplers and Metropolis algorithms; these models, however, often have many parameters, and convergence of the seemingly most natural Gibbs and Metropolis algorithms can sometimes be slow. We examine solutions that involve repar ..."
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Cited by 8 (4 self)
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Hierarchical linear and generalized linear models can be fit using Gibbs samplers and Metropolis algorithms; these models, however, often have many parameters, and convergence of the seemingly most natural Gibbs and Metropolis algorithms can sometimes be slow. We examine solutions that involve reparameterization and overparameterization. We begin with parameter expansion using working parameters, a strategy developed for the EM algorithm by Meng and van Dyk (1997) and Liu, Rubin, and Wu (1998). This strategy can lead to algorithms that are much less susceptible to becoming stuck near zero values of the variance parameters than are more standard algorithms. Second, we consider a simple rotation of the regression coefficients based on an estimate of their posterior covariance matrix. This leads to a Gibbs algorithm based on updating the transformed parameters one at a time or a Metropolis algorithm with vector jumps; either of these algorithms can perform much better (in terms of total CPU time) than the two standard algorithms: oneatatime updating of untransformed parameters or vector updating using a linear regression at each step. We present an innovative evaluation of the algorithms in terms of how quickly they can get away from remote areas of parameter space, along with some more standard evaluation of computation and convergence speeds. We illustrate our methods with examples from our applied work. Our ultimate goal is to develop a fast and reliable method for fitting a hierarchical linear model as easily as one can now fit a nonhierarchical model, and to increase understanding of Gibbs samplers for hierarchical models in general. Keywords: Bayesian computation, blessing of dimensionality, Markov chain Monte Carlo, multilevel modeling, mixed effects models, PXEM algorithm, random effects regression, redundant
Using redundant parameterizations to fit hierarchical models
 Journal of Computational and Graphical Statistics
, 2008
"... Hierarchical linear and generalized linear models can be fit using Gibbs samplers and Metropolis algorithms; these models, however, often have many parameters, and convergence of the seemingly most natural Gibbs and Metropolis algorithms can sometimes be slow. We examine solutions that involve repar ..."
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Cited by 5 (0 self)
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Hierarchical linear and generalized linear models can be fit using Gibbs samplers and Metropolis algorithms; these models, however, often have many parameters, and convergence of the seemingly most natural Gibbs and Metropolis algorithms can sometimes be slow. We examine solutions that involve reparameterization and overparameterization. We begin with parameter expansion using working parameters, a strategy developed for the EM algorithm. This strategy can lead to algorithms that are much less susceptible to becoming stuck near zero values of the variance parameters than are more standard algorithms. Second, we consider a simple rotation of the regression coefficients based on an estimate of their posterior covariance matrix. This leads to a Gibbs algorithm based on updating the transformed parameters one at a time or a Metropolis algorithm with vector jumps; either of these algorithms can perform much better (in terms of total CPU time) than the two standard algorithms: oneatatime updating of untransformed parameters or vector updating using a linear regression at each step. We present an innovative evaluation of the algorithms in terms of how quickly they can get away from remote areas of parameter space, along with some
Avoiding model selection in Bayesian social research
 Sociological Methodology
, 1994
"... Introduction Raftery's paper addresses two important problems in the statistical analysis of social science data: (1) choosing an appropriate model when so much data are available that standard Pvalues reject all parsimonious models; and (2) making estimates and predictions when there are not enou ..."
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Cited by 3 (1 self)
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Introduction Raftery's paper addresses two important problems in the statistical analysis of social science data: (1) choosing an appropriate model when so much data are available that standard Pvalues reject all parsimonious models; and (2) making estimates and predictions when there are not enough data available to fit the desired model using standard techniques. For both problems, we agree with Raftery that classical frequentist methods fail and that Raftery's suggested methods based on BIC can point in better directions. Nevertheless, we disagree with his solutions because, in principle, they are still directed offtarget and only by serendipity manage to hit the target in special circumstances. Our primary criticisms of Raftery's proposals are that (1) he promises the impossible: the selection of a model that is adequate for specific purposes without consideration of those purposes; and (2) he uses the same limited tool for model averaging as for model selection, thereby
Regression Models for Decision Making: A CostBenefit Analysis of Incentives in Telephone Surveys
, 2000
"... A standard method for reducing survey nonresponse is to offer incentives to survey participants. We reanalyze the data from a recent metaanalysis (Singer et al., 1999), using a hierarchical regression model, in order to estimate the effects of prepaid and postpaid incentives for facetoface and ..."
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Cited by 1 (1 self)
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A standard method for reducing survey nonresponse is to offer incentives to survey participants. We reanalyze the data from a recent metaanalysis (Singer et al., 1999), using a hierarchical regression model, in order to estimate the effects of prepaid and postpaid incentives for facetoface and telephone surveys. We then apply the results of our fitted model to the New York City Social Indicators Survey, a biennial telephone survey with a high nonresponse rate. We consider the balance of estimated costs, cost savings, and response rate for different choices of incentives. In general, we propose a methodology for evaluating some costbenefit decisions in sample survey design. Keywords: decision analysis, hierarchical linear regression, informal Bayes, metaanalysis, survey nonresponse 1 Introduction What with over 90% of U.S. households having telephones, and the convenience of random digit dialing and computer assisted interviewing, telephone interviewing has become increa...
Regression Modeling and MetaAnalysis
 Journal of Business & Economic Statistics
, 2003
"... this article we attempt to provide an approach to quantifying the costs and benefits of incentives, as a means of assisting in the decision of whether and how to apply an incentive in a particular telephone survey. We proceed in two steps. In Section 2 we reanalyze the data from the comprehensive me ..."
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this article we attempt to provide an approach to quantifying the costs and benefits of incentives, as a means of assisting in the decision of whether and how to apply an incentive in a particular telephone survey. We proceed in two steps. In Section 2 we reanalyze the data from the comprehensive metaanalysis of Singer, Van Hoewyk, Gebler, Raghunathan, and McGonagle (1999) of incentives in facetoface and telephone surveys and model the effect of incentives on response rates as a function of timing and amount of incentive and descriptors of the survey. In Section 3 we apply the model estimates to the cost structure of the New York City Social Indicators Survey, a biennial study with a nonresponse rate in the 50% range. In Section 4 we consider how these ideas can be applied generally and discuss limitations of our approach
NORMALIZING CONSTANTS
"... Abstract. Computing (ratios of) normalizing constants of probability models is a fundamental computational problem for many statistical and scientific studies. Monte Carlo simulation is an effective technique, especially with complex and highdimensional models. This paper aims to bring to the atten ..."
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Abstract. Computing (ratios of) normalizing constants of probability models is a fundamental computational problem for many statistical and scientific studies. Monte Carlo simulation is an effective technique, especially with complex and highdimensional models. This paper aims to bring to the attention of general statistical audiences of some effective methods originating from theoretical physics and at the same time to explore these methods from a more statistical perspective, through establishing theoretical connections and illustrating their uses with statistical problems. We show that the acceptance ratio method and thermodynamic integration are natural generalizations of importance sampling, which is most familiar to statistical audiences. The former generalizes importance sampling through the use of a single “bridge ” density and is thus a case of bridge sampling in the sense of Meng and Wong. Thermodynamic integration, which is also known in the numerical analysis literature as Ogata’s method for highdimensional integration, corresponds to the use of infinitely many and continuously connected bridges (and thus a “path”). Our path sampling formulation offers more flexibility and thus potential efficiency to thermodynamic integration, and the search of optimal paths turns out to have close connections with the Jeffreys prior density and the Rao and Hellinger distances between two densities. We provide an informative theoretical example as well as two empirical examples (involving 17 to 70dimensional integrations) to illustrate the potential and implementation of path sampling. We also discuss some open problems.