Combining Expert Opinions in Prior Elicitation

Albert, Isabelle; Donnet, Sophie; Guihenneuc‐Jouyaux, Chantal; Low‐Choy, Samantha; Mengersen, Kerrie; Rousseau, Judith

doi:10.1214/12-ba717

Cited by 101 publications

(101 citation statements)

References 21 publications

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“…There is a reasonably well-developed literature on methods designed to elicit priors from people (e.g., Albert et al, 2012;Garthwaite, Kadane, & O'Hagan, 2005;Kadane & Wolfson, 1998;O'Hagan et al, 2006). These methods are used quite extensively in modeling in some empirical sciences, but do not seem to be used routinely in cognitive modeling.…”

Section: Elicitationmentioning

confidence: 99%

Determining informative priors for cognitive models

2017

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The development of cognitive models involves the creative scientific formalization of assumptions, based on theory, observation, and other relevant information. In the Bayesian approach to implementing, testing, and using cognitive models, assumptions can influence both the likelihood function of the model, usually corresponding to assumptions about psychological processes, and the prior distribution over model parameters, usually corresponding to assumptions about the psychological variables that influence those processes. The specification of the prior is unique to the Bayesian context, but often raises concerns that lead to the use of vague or non-informative priors in cognitive modeling. Sometimes the concerns stem from philosophical objections, but more often practical difficulties with how priors should be determined are the stumbling block. We survey several sources of information that can help to specify priors for cognitive models, discuss some of the methods by which this information can be formalized in a prior distribution, and identify a number of benefits of including informative priors in cognitive modeling. Our discussion is based on three illustrative cognitive models, involving memory retention, categorization, and decision making.

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Section: Elicitationmentioning

confidence: 99%

Determining informative priors for cognitive models

2017

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“…The least-squares optimization enables fast and accurate computation. See, for example, Albert et al (2012) and the references therein. If a Dirichlet prior is to be encoded, the parameters α i = α i and β i =β i will be directly reconciled to obtain the Dirichlet hyperparameters in Sect.…”

Section: Encoding the Hyperparameters Of The Beta Marginal Distributionsmentioning

confidence: 99%

“…The usage of least-squares techniques for reconciliation has been discussed in Albert et al (2012). Our proposed method differs from those of Bunn (1978) and Chaloner and Duncan (1987) as we require only medians and quartiles to be assessed.…”

Section: Introductionmentioning

confidence: 99%

Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models

Elfadaly

Garthwaite

2016

Stat Comput

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In this paper, we propose novel methods of quantifying expert opinion about prior distributions for multinomial models. Two different multivariate priors are elicited using median and quartile assessments of the multinomial probabilities. First, we start by eliciting a univariate beta distribution for the probability of each category. Then we elicit the hyperparameters of the Dirichlet distribution, as a tractable conjugate prior, from those of the univariate betas through various forms of reconciliation using least-squares techniques. However, a multivariate copula function will give a more flexible correlation structure between multinomial parameters if it is used as their multivariate prior distribution. So, second, we use beta marginal distributions to construct a Gaussian copula as a multivariate normal distribution function that binds these marginals and expresses the dependence structure between them. The proposed method elicits a positive-definite correlation matrix of this Gaussian copula. The two proposed methods are designed to be used through interactive graphical software written in Java.

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“…Indeed, the assignment of each expert to a specific group might be rather difficult and somewhat arbitrary. This is why we prefer a mixture model to a hierarchical random-effect model, as used by Albert et al (2012). Within each group j, the members' opinions are sampled from a multivariate Gaussian distribution, centered on μ j and having covariance matrix Σ j , with j = 1, .…”

Section: The Proposed Approachmentioning

confidence: 99%

“…When opinions are elicited on several objects and at different time points (as in our case), the choice of a multivariate normal distribution requires the specification of a large number of parameters: marginal means and variances, and correlations between objects and between experts. Albert et al (2012) suggested a hierarchical random-effects model as a more parsimonious approach, in the sense of the number of parameters to be specified, especially when the number of experts is large. Here, we suggest implicitly deriving the dependence structure of the expert evaluations by using a mixture model.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Population Forecasting Based on Combinations of Expert Evaluations Within the Bayesian Paradigm

2014

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This article suggests a procedure to derive stochastic population forecasts adopting an expert-based approach. As in previous work by Billari et al. (2012), experts are required to provide evaluations, in the form of conditional and unconditional scenarios, on summary indicators of the demographic components determining the population evolution: that is, fertility, mortality, and migration. Here, two main purposes are pursued. First, the demographic components are allowed to have some kind of dependence. Second, as a result of the existence of a body of shared information, possible correlations among experts are taken into account. In both cases, the dependence structure is not imposed by the researcher but rather is indirectly derived through the scenarios elicited from the experts. To address these issues, the method is based on a mixture model, within the so-called SupraBayesian approach, according to which expert evaluations are treated as data. The derived posterior distribution for the demographic indicators of interest is used as forecasting distribution, and a Markov chain Monte Carlo algorithm is designed to approximate this posterior. This article provides the questionnaire designed by the authors to collect expert opinions. Finally, an application to the forecast of the Italian population from 2010 to 2065 is proposed.

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Combining Expert Opinions in Prior Elicitation

Cited by 101 publications

References 21 publications

Determining informative priors for cognitive models

Determining informative priors for cognitive models

Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models

Stochastic Population Forecasting Based on Combinations of Expert Evaluations Within the Bayesian Paradigm

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