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Abstract This paper extends the application of quantile-based Bayesian inference to probability distributions defined in terms of quantiles of observable quantities. Quantile-parameterized distributions are characterized by high shape flexibility and parameter interpretability, making them useful for eliciting information about observables. To encode uncertainty in the quantiles elicited from experts, we propose a Bayesian model based on the metalog distribution and a variant of the Dirichlet prior. We discuss the resulting hybrid expert elicitation protocol, which aims to characterize uncertainty in parameters by asking questions about observable quantities. We also compare and contrast this approach with parametric and predictive elicitation methods.
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This content will become publicly available on March 31, 2026
Quantile-Parameterized Distributions for Expert Knowledge Elicitation
This paper provides a comprehensive overview of quantile-parameterized distributions (QPDs) as a tool for capturing expert predictions and parametric judgments. We survey a range of methods for constructing distributions that are parameterized by a set of quantile-probability pairs and describe an approach to generalizing them to enhance their tail flexibility. Furthermore, we explore the extension of QPDs to the multivariate setting, surveying the approaches to construct bivariate distributions, which can be adopted to obtain distributions with quantile-parameterized margins. Through this review and synthesis of the previously proposed methods, we aim to enhance the understanding and utilization of QPDs in various domains. Funding: U. Sahlin was funded by the Crafoord Foundation [ref 20200626]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2024.0219 .
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- Award ID(s):
- 2153019
- PAR ID:
- 10611206
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- Decision Analysis
- ISSN:
- 1545-8490
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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