Daniel Goodman’s empirical approach to Bayesian statistics

30 Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty 31 about the state of knowledge. Bayesian statistics has often been associated with the idea that 32 knowledge is subjective and that a probability distribution represents a personal degree of belief. 33 Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He 34 sought to ground his Bayesian approach in data, and advocated the construction of a prior as an 35 empirical histogram of “similar” cases. In this way, the posterior distribution that results from a 36 Bayesian analysis combined comparable previous data with case-specific current data, using 37 Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it 38 was difficult in practice. If based on a true representation of our knowledge and uncertainty, 39 Goodman argued that risk assessment and decision-making could be an exact science, despite the 40 uncertainties. In his view, Bayesian statistics is a critical component of this science because a 41 Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained 42 that the Bayesian machinery, following the rules of conditional probability, offered the best 43 legitimate inference from available data. We give an example of an informative prior in a recent 44 study of Steller sea lion spatial use patterns in Alaska. 45