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February 2018 Effects of prior distributions: An application to pipedwater demand
Andrés Ramírez Hassan, Luis Pericchi
Braz. J. Probab. Stat. 32(1): 1-19 (February 2018). DOI: 10.1214/16-BJPS329

Abstract

In this paper, we analyze the effect on posterior parameter distributions of four possible alternative prior distributions, namely Normal-Inverse Gamma, Normal-Scaled Beta two, Student’s $t$-Inverse Gamma and Student’s $t$-Scaled Beta two. We show the effects of these prior distributions when there is apparently conflict between the sample information and the elicited hyperparameters. In particular, we show that there is not systematic differences of posterior parameter distributions associated with these four priors using data of piped water demand in a linear model with autoregressive errors. To test the hypothesis that this result is due to using a moderate sample size and a relatively high level of expert’s uncertainty, we perform some simulation exercises assuming smaller sample sizes and lower expert’s uncertainty. We obtain the general same pattern, although Student’s $t$ models are slightly less affected by prior information when there is a high level of expert’s certainty, and Scaled Beta two models exhibit a higher level of posterior dispersion of the variance parameter.

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Andrés Ramírez Hassan. Luis Pericchi. "Effects of prior distributions: An application to pipedwater demand." Braz. J. Probab. Stat. 32 (1) 1 - 19, February 2018. https://doi.org/10.1214/16-BJPS329

Information

Received: 1 June 2015; Accepted: 1 July 2016; Published: February 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06973946
MathSciNet: MR3770861
Digital Object Identifier: 10.1214/16-BJPS329

Keywords: autoregressive model , Bayesian analysis , elicitation , robustness analysis

Rights: Copyright © 2018 Brazilian Statistical Association

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Vol.32 • No. 1 • February 2018
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