SPEAKER: Robin Gong, Assistant Professor, Statistics, Rutgers University
TITLE : “Modeling uncertainty with sets of probabilities”
ABSTRACT: In statistical modeling, uncertainty cannot always be faithfully captured by a single probability distribution. The modeler can be unsure how to specify a prior for a Bayesian model, or to assume a probabilistic mechanism for the missing data, or to quantify uncertainty for an under-identified model parameter. In this talk, I motivate sets of probabilities as an attractive modeling strategy, which encodes low-resolution information in both the data and the model spaces with little need to concoct unwarranted assumptions. I present a Dempster-Shafer model for multinomial parameter estimation, which delivers essentially prior-free posterior inference and can be understood as versions of differentially private Bayesian histogram estimation. I discuss challenges that arise with the employment of belief and capacity functions, special cases of sets of probabilities, and how the choice of conditioning rules reconciles among a trio of unsettling posterior phenomena: dilation, contraction and sure loss. These findings underscores the invaluable role of judicious judgment in handling low-resolution probabilistic information.
DATE: Thursday, January 24th, 4:10pm
LOCATION: MSB 1147, Colloquium Room
REFRESHMENTS: 3:30pm MSB 4110 (4th floor lounge)
STA 290 Seminar List: https://statistics.ucdavis.edu/seminars