Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection
Abstract
Bayesian model evidence (BME) is a measure of the average fit of a model to observation data given all the parameter values that the model can assume. By accounting for the trade-off between goodness-of-fit and model complexity, BME is used for model selection and model averaging purposes. For strict Bayesian computation, the theoretically unbiased Monte Carlo based numerical estimators are preferred over semi-analytical solutions. This study examines five BME numerical estimators and asks how accurate estimation of the BME is important for penalizing model complexity. The limiting cases for numerical BME estimators are the prior sampling arithmetic mean estimator (AM) and the posterior sampling harmonic mean (HM) estimator, which are straightforward to implement, yet they result in underestimation and overestimation, respectively. We also consider the path sampling methods of thermodynamic integration (TI) and steppingstone sampling (SS) that sample multiple intermediate distributions that link the prior and the posterior. Although TI and SS are theoretically unbiased estimators, they could have a bias in practice arising from numerical implementation. For example, sampling errors of some intermediate distributions can introduce bias. We propose a variant of SS, namely the multiple one-steppingstone sampling (MOSS) that is less sensitive to sampling errors. We evaluate thesemore »
- Authors:
-
- Univ. of Hawaii at Manoa, Honolulu, HI (United States)
- Florida State Univ., Tallahassee, FL (United States)
- Publication Date:
- Research Org.:
- Florida State Univ., Tallahassee, FL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER); National Science Foundation (NSF)
- OSTI Identifier:
- 1611030
- Grant/Contract Number:
- SC0008272; SC0019438; OIA-1557349; EAR-1552329
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Water (Basel)
- Additional Journal Information:
- Journal Name: Water (Basel); Journal Volume: 11; Journal Issue: 8; Journal ID: ISSN 2073-4441
- Publisher:
- MDPI
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 54 ENVIRONMENTAL SCIENCES; groundwater transport; Bayesian; model selection; Bayesian model averaging; modeling; model complexity; Bayesian model evidence; marginal likelihood
Citation Formats
Elshall, Ahmed S., and Ye, Ming. Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection. United States: N. p., 2019.
Web. doi:10.3390/w11081579.
Elshall, Ahmed S., & Ye, Ming. Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection. United States. https://doi.org/10.3390/w11081579
Elshall, Ahmed S., and Ye, Ming. Tue .
"Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection". United States. https://doi.org/10.3390/w11081579. https://www.osti.gov/servlets/purl/1611030.
@article{osti_1611030,
title = {Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection},
author = {Elshall, Ahmed S. and Ye, Ming},
abstractNote = {Bayesian model evidence (BME) is a measure of the average fit of a model to observation data given all the parameter values that the model can assume. By accounting for the trade-off between goodness-of-fit and model complexity, BME is used for model selection and model averaging purposes. For strict Bayesian computation, the theoretically unbiased Monte Carlo based numerical estimators are preferred over semi-analytical solutions. This study examines five BME numerical estimators and asks how accurate estimation of the BME is important for penalizing model complexity. The limiting cases for numerical BME estimators are the prior sampling arithmetic mean estimator (AM) and the posterior sampling harmonic mean (HM) estimator, which are straightforward to implement, yet they result in underestimation and overestimation, respectively. We also consider the path sampling methods of thermodynamic integration (TI) and steppingstone sampling (SS) that sample multiple intermediate distributions that link the prior and the posterior. Although TI and SS are theoretically unbiased estimators, they could have a bias in practice arising from numerical implementation. For example, sampling errors of some intermediate distributions can introduce bias. We propose a variant of SS, namely the multiple one-steppingstone sampling (MOSS) that is less sensitive to sampling errors. We evaluate these five estimators using a groundwater transport model selection problem. SS and MOSS give the least biased BME estimation at an efficient computational cost. If the estimated BME has a bias that covariates with the true BME, this would not be a problem because we are interested in BME ratios and not their absolute values. On the contrary, the results show that BME estimation bias can be a function of model complexity. Thus, biased BME estimation results in inaccurate penalization of more complex models, which changes the model ranking. This was less observed with SS and MOSS as with the three other methods.},
doi = {10.3390/w11081579},
journal = {Water (Basel)},
number = 8,
volume = 11,
place = {United States},
year = {Tue Jul 30 00:00:00 EDT 2019},
month = {Tue Jul 30 00:00:00 EDT 2019}
}
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