Daniel Goodman’s empirical approach to Bayesian statistics
- Published
- Accepted
- Subject Areas
- Conservation Biology, Ecology, Mathematical Biology, Science Policy, Statistics
- Keywords
- Bayesian inference, structured decision making, uncertainty, hierarchical Bayes, informative priors, natural resource management
- Copyright
- © 2016 Gerrodette et al.
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ PrePrints) and either DOI or URL of the article must be cited.
- Cite this article
- 2016. Daniel Goodman’s empirical approach to Bayesian statistics. PeerJ PrePrints 4:e1755v1 https://doi.org/10.7287/peerj.preprints.1755v1
Abstract
Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty about the state of knowledge. Bayesian statistics has often been associated with the idea that knowledge is subjective and that a probability distribution represents a personal degree of belief. Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He sought to ground his Bayesian approach in data, and advocated the construction of a prior as an empirical histogram of “similar” cases. In this way, the posterior distribution that results from a Bayesian analysis combined comparable previous data with case-specific current data, using Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it was difficult in practice. If based on a true representation of our knowledge and uncertainty, Goodman argued that risk assessment and decision-making could be an exact science, despite the uncertainties. In his view, Bayesian statistics is a critical component of this science because a Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained that the Bayesian machinery, following the rules of conditional probability, offered the best legitimate inference from available data. We give an example of an informative prior in a recent study of Steller sea lion spatial use patterns in Alaska.
Author Comment
This is a preprint submission to PeerJ Preprints. The article was prepared as a contribution to the Daniel Goodman Memorial Symposium, Decision-making under Uncertainty: Risk Assessment and the Best Available Science, held March 20-21, 2014, at the Museum of the Rockies, Montana State University, Bozeman, Montana, USA. The symposium was held in honor of the late Dr. Daniel Goodman, professor of biology and ecology at Montana State University.