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Effects of prior distributions: An application to pipedwater demand
- Source :
- Braz. J. Probab. Stat. 32, no. 1 (2018), 1-19
- Publication Year :
- 2018
- Publisher :
- Institute of Mathematical Statistics, 2018.
-
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.
- Subjects :
- elicitation
Statistics and Probability
Hyperparameter
010504 meteorology & atmospheric sciences
Bayesian probability
Bayesian analysis
Linear model
Sample (statistics)
Autoregressive model
01 natural sciences
010104 statistics & probability
Sample size determination
robustness analysis
Prior probability
Statistics
Statistical dispersion
0101 mathematics
0105 earth and related environmental sciences
Mathematics
Subjects
Details
- ISSN :
- 01030752
- Volume :
- 32
- Database :
- OpenAIRE
- Journal :
- Brazilian Journal of Probability and Statistics
- Accession number :
- edsair.doi.dedup.....7045a57a58797355d682755115621d72