Hybrid elicitation and quantile-parametrized likelihood

Perepolkin, Dmytro; Goodrich, Benjamin; Sahlin, Ullrika

doi:10.31219/osf.io/paby6

Cited by 3 publications

(9 citation statements)

References 20 publications

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“…Through experimentation involving 103 judges, Abbas et al (2008) showed "slight but consistent superiority" for the variable interval method along several dimensions such as accuracy and precision of the estimated fractiles. It is also possible to jointly ask both quantiles and probability, a quantile-probability tuple (Perepolkin et al, 2021), in which case the method is referred to as PV-method (Spetzler and Holstein, 1975).…”

Section: Univariate Priormentioning

confidence: 99%

“…A challenge in doing elicitation in the observable space is the difficulty to separate two sources of randomness: due to θ and due to y (Garthwaite et al, 2005;Perepolkin et al, 2021). There are some solutions to that, for instance, Kadane and Winkler (1988) proposed to the expert to consider only the mean ȳ, and then conduct other assessment tasks to elicit the randomness in y.…”

Section: Elicitation In Observable Spacementioning

confidence: 99%

“…• Quantile-probability tuples with indirect Bayesian inference (Perepolkin et al, 2021). In their simple version (Perepolkin et al, 2021, Sec.…”

Section: Bayesian Treatment Of the Expert In Prior Elicitationmentioning

confidence: 99%

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Prior knowledge elicitation: The past, present, and future

Mikkola¹,

Martin²,

Chandramouli³

et al. 2021

Preprint

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Specification of the prior distribution for a Bayesian model is a central part of the Bayesian workflow for data analysis, but it is often difficult even for statistical experts. Prior elicitation transforms domain knowledge of various kinds into well-defined prior distributions, and offers a solution to the prior specification problem, in principle. In practice, however, we are still fairly far from having usable prior elicitation tools that could significantly influence the way we build probabilistic models in academia and industry. We lack elicitation methods that integrate well into the Bayesian workflow and perform elicitation efficiently in terms of costs of time and effort. We even lack a comprehensive theoretical framework for understanding different facets of the prior elicitation problem.Why are we not widely using prior elicitation? We analyze the state of the art by identifying a range of key aspects of prior knowledge elicitation, from properties of the modelling task and the nature of the priors to the form of interaction with the expert. The existing prior elicitation literature is reviewed and categorized in these terms. This allows recognizing under-studied directions in prior elicitation research, finally leading to a proposal of several new avenues to improve prior elicitation methodology.

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Section: Univariate Priormentioning

confidence: 99%

Section: Elicitation In Observable Spacementioning

confidence: 99%

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Prior knowledge elicitation: The past, present, and future

Mikkola¹,

Martin²,

Chandramouli³

et al. 2021

Preprint

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show abstract

“…This direct approach requires no translation. For example, the Bayesian quantile-parameterised likelihood (Hadlock, 2017;Keelin and Powley, 2011) approach of Perepolkin et al (2021) involves updating directly elicited properties of a phenomena, it is unsurprising that such information is associable with many prior distributions.…”

Section: Introductionmentioning

confidence: 99%

Translating predictive distributions into informative priors

Manderson¹,

Goudie²

2023

Preprint

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When complex Bayesian models exhibit implausible behaviour, one solution is to assemble available information into an informative prior. Challenges arise as prior information is often only available for the observable quantity, or some model-derived marginal quantity, rather than directly pertaining to the natural parameters in our model. We propose a method for translating available prior information, in the form of an elicited distribution for the observable or model-derived marginal quantity, into an informative joint prior. Our approach proceeds given a parametric class of prior distributions with as yet undetermined hyperparameters, and minimises the difference between the supplied elicited distribution and corresponding prior predictive distribution. We employ a global, multi-stage Bayesian optimisation procedure to locate optimal values for the hyperparameters. Three examples illustrate our approach: a nonlinear regression model; a setting in which prior information pertains to R 2 -a model-derived quantity; and a cure-fraction survival model, where censoring implies that the observable quantity is a priori a mixed discrete/continuous quantity.

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“…We believe that the primary utility of QPDs lies in their ability to simplify the specification of probability distributions for model parameters, known as prior elicitation (Mikkola et al, 2021). However, these same distributions can also be employed to describe an expert's predictions for the next observation, referred to as predictive elicitation (Winkler, 1980;Kadane, 1980;Akbarov, 2009;Hartmann et al, 2020), or to capture both uncertainty and variability through a two-dimensional probability distribution in hybrid elicitation (Perepolkin et al, 2021a). Through our comprehensive review and identification of research gaps, we aim to contribute to the development of flexible and extensible distributions that can effectively capture expert knowledge.…”

Section: Introductionmentioning

confidence: 99%

Quantile-parameterized distributions for expert knowledge elicitation

Perepolkin,

Lindsröm,

Sahlin

2023

Preprint

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This paper presents a comprehensive overview of quantile-parameterized distributions (QPDs) as a powerful tool for capturing expert predictions and parametric judgments. We survey various types of QPDs covered in the literature and focus on the Myerson distribution as the simplest method of parameterizing a distribution by a set of quantile-probability pairs. We propose the generalization of the Myerson distribution to increase the flexibility of its tails. Additionally, we explore the extension of QPDs to the multivariate setting, discussing methods for constructing bivariate distributions with quantile-parameterized margins.

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Hybrid elicitation and quantile-parametrized likelihood

Cited by 3 publications

References 20 publications

Prior knowledge elicitation: The past, present, and future

Prior knowledge elicitation: The past, present, and future

Translating predictive distributions into informative priors

Quantile-parameterized distributions for expert knowledge elicitation

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