B0311
Title: Exploring model uncertainty using linear programming
Authors: Hari Iyer - National Institute of Standars and Technology (United States) [presenting]
Steve Lund - National Institute of Standards and Technology (United States)
David Newton - National Institute of Standards and Technology (United States)
Abstract: Given independent, identically distributed realizations $x_1, x_2, \ldots, x_n$ from an unknown distribution, statisticians use tools at their disposal and, typically, find a distribution that they view as reasonably capable of producing data like that observed. This fitted distribution is then used to make inferences regarding functions of model parameters that may be of interest in a given application. Besides finding a point estimate for a quantity of interest, they also report a confidence interval to express the range of values thought to be plausible for the quantity of interest. However, this range, most often, only accounts for sampling variability and does not adequately address model uncertainty. Even techniques such as model averaging only partially address the issue of model uncertainty. An approach is described that can more fully address the issue of modelling uncertainty. The approach uses linear programming methods to find a range of plausible values for the quantity of interest. The range of "all plausible" values for the quantity of interest will be at least as extreme as the lower and upper limits provided by the "range analysis" approach. The method is illustrated using an example from DNA mixture interpretation from statistical forensics.
