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12
Statistical Methods for Eliciting Probability Distributions
 Journal of the American Statistical Association
, 2005
"... Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatterexpert colleagues. This paper reviews the stateoftheart, reflecting the experience of statisticia ..."
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Cited by 61 (3 self)
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Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatterexpert colleagues. This paper reviews the stateoftheart, reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively, and how they respond to questions about that information. In a discussion of the elicitation process, the first issue to address is what it means for an elicitation to be successful, i.e. what criteria should be employed? Our answer is that a successful elicitation faithfully represents the opinion of the person being elicited. It is not necessarily “true ” in some objectivistic sense, and cannot be judged that way. We see elicitation as simply part of the process of statistical modeling. Indeed in a hierarchical model it is ambiguous at which point the likelihood ends and the prior begins. Thus the same kinds of judgment that inform statistical modeling in general also inform elicitation of prior distributions.
What to do about missing values in time series crosssection data
, 2009
"... Applications of modern methods for analyzing data with missing values, based primarily on multiple imputation, have in the last halfdecade become common in American politics and political behavior. Scholars in this subset of political science have thus increasingly avoided the biases and inefficien ..."
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Cited by 29 (6 self)
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Applications of modern methods for analyzing data with missing values, based primarily on multiple imputation, have in the last halfdecade become common in American politics and political behavior. Scholars in this subset of political science have thus increasingly avoided the biases and inefficiencies caused by ad hoc methods like listwise deletion and best guess imputation. However, researchers in much of comparative politics and international relations, and others with similar data, have been unable to do the same because the best available imputation methods work poorly with the timeseries cross section data structures common in these fields. Weattempttorectify this situation with three related developments. First, we build a multiple imputation model that allows smooth time trends, shifts across crosssectional units, and correlations over time and space, resulting in far more accurate imputations. Second, we enable analysts to incorporate knowledge from area studies experts via priors on individual missing cell values, rather than on difficulttointerpret model parameters. Third, because these tasks could not be accomplished within existing imputation algorithms, in that they cannot handle as many variables as needed even in the simpler crosssectional data for which they were designed, we also develop a new algorithm that substantially expands the range of computationally feasible data types and sizes for which multiple imputation can be used. These developments also make it possible to implement the methods introduced here in freely available open source software that is considerably more reliable than existing algorithms. We develop an approach to analyzing data with
Elicited Priors for Bayesian Model Specifications
 in Political Science Research. Forthcoming, Journal of Politics
, 2005
"... We explain how to use elicited priors in Bayesian political science research. These are a form of prior information produced by previous knowledge from structured interviews with subjective area experts who have little or no concern for the statistical aspects of the project. The purpose is to intro ..."
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Cited by 11 (4 self)
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We explain how to use elicited priors in Bayesian political science research. These are a form of prior information produced by previous knowledge from structured interviews with subjective area experts who have little or no concern for the statistical aspects of the project. The purpose is to introduce qualitative and areaspecific information into an empirical model in a systematic and organized manner in order to produce parsimonious yet realistic implications. Currently, there is no work in political science that articulates elicited priors in a Bayesian specification. We demonstrate the value of the approach by applying elicited priors to a problem in judicial comparative politics using data and elicitations we collected in Nicaragua. As quantitative political research becomes increasingly sophisticated, the more complex, but more capable, Bayesian approach is likely to grow in popularity. The Bayesian inferential engine is a coherent set of axioms that converts prior information to posterior evidence by conditioning on observed data. Thus, stipulating prior distributions for unknown quantities is a requirement, and this requirement has been a longstanding source of controversy. Bayesians statistics provides a number of ways to define prior information, and the strength of these
Highly Informative Priors
, 1985
"... INTRODUCTION The statistical problems envisaged in our pedagogy are almost always ones in which we acquire new data D that give evidence concerning some hypotheses H; H 0 ; : : : (this includes parameter estimation, since H might be the statement that a parameter lies in a certain interval); and w ..."
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Cited by 3 (0 self)
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INTRODUCTION The statistical problems envisaged in our pedagogy are almost always ones in which we acquire new data D that give evidence concerning some hypotheses H; H 0 ; : : : (this includes parameter estimation, since H might be the statement that a parameter lies in a certain interval); and we make inferences about them solely from the data. Indeed, Fisher's maxim, "Let the data speak for themselves" seems to imply that it would be wrong  a violation of "scientific objectivity"  to allow ourselves to be influenced by other considerations such as prior knowledge about H . Yet the very act of choosing a model (i.e. a sampling distribution conditional on H) is a means of expressing some kind of prior knowledge about the existence and nature of H , and its observable effects. This was noted by John Tukey (1978), who observed that sampling theory is in the curious
“I can name that Bayesian Network in Two Matrixes!”
"... The traditional approach to building Bayesian networks is to build the graphical structure using a graphical editor and then add probabilities using a separate spreadsheet for each node. This can make it difficult for a design team to get an impression of the total evidence provided by an assessment ..."
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Cited by 2 (2 self)
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The traditional approach to building Bayesian networks is to build the graphical structure using a graphical editor and then add probabilities using a separate spreadsheet for each node. This can make it difficult for a design team to get an impression of the total evidence provided by an assessment, especially if the Bayesian network is split into many fragments to make it more manageable. Using the design patterns commonly used to build Bayesian networks for educational assessments, the collection of networks necessary can be specified using two matrixes. An inverse covariance matrix among the proficiency variables (the variables which are the target of interest) specifies the graphical structure and relation strength of the proficiency model. A Qmatrix — an incidence matrix whose rows represent observable outcomes from assessment tasks and whose columns represent proficiency variables — provides the graphical structure of the evidence models (graph fragments linking proficiency variables to observable outcomes). The Qmatrix can be augmented to provide details of relationship strengths and provide a high level overview of the kind of evidence available in the assessment. The representation of the model using matrixes means that the bulk of the specification work can be done using a desktop spreadsheet program and does not require specialized software, facilitating collaboration with external experts. The design idea is illustrated with some examples from prior assessment design projects.
Elicitation
, 2004
"... Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatterexpert colleagues. This paper reviews the stateoftheart, reflecting both the experience of statis ..."
Abstract
 Add to MetaCart
Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatterexpert colleagues. This paper reviews the stateoftheart, reflecting both the experience of statisticians and the fruits of a long line of psychological research into how people represent uncertain information cognitively, and how they respond to questions about that information. In a discussion of the elicitation process, the first issue to address is what it means for an elicitation to be successful, i.e. what criteria should be employed? Our answer is that a successful elicitation faithfully represents the opinion of the person being elicited. It is not necessarily “true ” in some objectivistic sense, and cannot be judged that way. We see elicitation as simply part of the process of statistical modeling. Indeed in a hierarchical model it is ambiguous at which point the likelihood ends and the prior begins. Thus the same kinds of judgment that inform statistical modeling in general also inform elicitation of prior distributions.
What to Do about Missing Values in TimeSeries
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Honaker, James and Gary King. 2010. What to do about missing values in timeseries crosssection data. American Journal of ..."
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Honaker, James and Gary King. 2010. What to do about missing values in timeseries crosssection data. American Journal of
Expected Posterior Prior Distributions for Model Selection
"... Consider the problem of comparing parametric models M 1 ; : : : ; M k , when at least one of the models has an improper prior ß N i (` i ). Using the Bayes factor for comparing among these is not feasible due to arbitrary multiplicative constants in ß N (` i ). In this work we suggest adjusting t ..."
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Consider the problem of comparing parametric models M 1 ; : : : ; M k , when at least one of the models has an improper prior ß N i (` i ). Using the Bayes factor for comparing among these is not feasible due to arbitrary multiplicative constants in ß N (` i ). In this work we suggest adjusting the initial priors for each model, ß N i , by ß i (` i ) = Z ß N i (` i jy )m (y )dy where m is a suitable predictive measure on (imaginary) training samples, y . The updated prior, ß , is called the expected posterior prior under m . Some properties of this approach include: (1) The resulting Bayes factors depend only on sufficient statistics. (2) The resulting Bayesian inference is coherent and allows for multiple comparisons. (3) In many cases, it is possible to find m such that, for a sample of minimal size, there is predictive matching for the comparisons of model M i to M j ,i.e., the Bayes factor B ij = 1. (4) In the case of nested models, where M 1 is ...
Chapter 1
"... Elicitation is the process of formulating a persons knowledge and beliefs about one or more uncertain quantities into a (joint) probability distribution for those quantities. In the context of Bayesian statistical analysis, it arises most usually as a method for specifying the prior distribution fo ..."
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Elicitation is the process of formulating a persons knowledge and beliefs about one or more uncertain quantities into a (joint) probability distribution for those quantities. In the context of Bayesian statistical analysis, it arises most usually as a method for specifying the prior distribution for one or more unknown
European Central Bank
, 2009
"... We discuss estimation of autoregressive models with a prior about initial growth rates of the modeled series. This prior allows to specify prior beliefs about the behavior of time series in a natural way and it serves to replace arbitrary assumptions on initial conditions. To implement this prior we ..."
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We discuss estimation of autoregressive models with a prior about initial growth rates of the modeled series. This prior allows to specify prior beliefs about the behavior of time series in a natural way and it serves to replace arbitrary assumptions on initial conditions. To implement this prior we develop a technique for translating priors about observables into priors about coefficients. The posterior mean is attractive even from the frequentist point of view: it is often less biased than the OLS estimate and has better frequentist risk than bias corrected estimates. We apply our prior to some empirical studies from the literature and find that it makes a big difference for the estimated