Elicited Priors for Bayesian Model Specifications in Political Science Research

Abstract

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 area-specific 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 long-standing source of controversy. Bayesian statistics provide a number of ways to define prior information, and the strength of these prior assertions can vary considerably within the same inferential framework.Recent Bayesian work in fields other than political science has exploited the elicited prior as a means of drawing information from subject-area experts with the goal of constructing a probability structure that reflects their specific qualitative knowledge, and perhaps experiential intuition, about the studied effects. These informed priors derive their name from the way in which the information is elicited from nonstatisticians who have a great deal of information about the substantive question but are not involved in the model construction process. Such experts can be physicians, policy-makers, theoretical economists, historians, previous study participants, outside experts, politicians, community leaders, and others.

Bayesian latent variable regression via Gibbs sampling: methodology and practical aspects

“…The second case study demonstrates that with a little effort, obtaining prior knowledge is certainly possible from existing sources. Methods for eliciting such information from domain experts are also available [34,35]. Analysis of the sensitivity of the model to available or elicited information via robust Bayes techniques may also be done.…”

“…If the prior mean ␣ T µ b = 0, and the prior covariance ␣ T Q b ␣ = I ⊗ k, then the conditional mean is the same as the solution for ridge regression [27], with the parameter λ = R y /k. With Equations (32) and (35), the MCMC step of the BLVR-S algorithm can be easily implemented for the case of a Gaussian prior. This conditional mean is also the MLE of β given y, ␣ and Z, which is also used in BLVR-OPT.…”

Eliciting expert judgements about a set of proportions

“…A third use is to express uncertainty about parameters in a decision analysis [7,9,30]. A substantial literature on elicitation is spread across many disciplines, including statistics, psychology, economics, decision-making and various application fields [1,6,18,24,27,31]. Where the results of elicitation have significant value it is usual for a facilitator, who is knowledgeable in probability, statistics and the processes of elicitation, to work with the expert(s) to elicit a suitable probability distribution [17].…”

Una propuesta metodológica para elicitar el vector de parámetros π de la distribución Multinomial

“…En contextos médicos se ha restringido en gran medida a las creencias a priori sobre los efectos de un tratamiento donde, las opiniones a priori se aplican al parámetro de interacción White et al (2005). En ciencias políticas Gill & Walker (2005) muestran unaútil aplicación de la elicitación de expertos para analizar la confianza de los ciudadanos nicaragüenses en el sistema judicial. Fox (1966), Gross (1971) y Van Noortwijk et al (1992) ponen la elicitación de expertos en el contexto de la confiabilidad.…”