Online Program

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Thursday, May 17
Machine Learning
Optimization
Thu, May 17, 10:30 AM - 12:00 PM
Lake Fairfax B
 

Plotting Two-Dimensional Confidence Regions (304486)

Presentation

Lawrence Leemis, College of William & Mary 
Andrew Loh, College of William & Mary 
*Christopher Weld, College of William & Mary 

Keywords: Graphical Methods, Parameter Estimation, Numerical Optimization

Plotting two-parameter confidence regions is non-trivial. Numerical methods often rely on a grid-like exploration of the parameter space to develop the corresponding contours of its confidence region, which is computationally expensive. A recent advance reduces the two-dimensional problem to a series of one-dimensional problems employing a trigonometric transformation of the parameter space that assigns an angle from the maximum likelihood estimator, and an unknown radial distance to its confidence region boundary. Although this paradigm shift improves plot accessibility by easing the computational burden by roughly three orders of magnitude, it is not terribly robust. Specifically, when parameters differ greatly in magnitude—which is not unusual for two-parameter distributions—the corresponding graphics are susceptible to computational inefficiencies and poor definition given a naive approach to its chosen set of angle values. This presentation improves the low cost two-dimensional radial profile log likelihood plot technique by (1) enhancing the existing algorithm to keep the confidence region boundary searches in the parameter space, and (2) selectively targeting points along the confidence region boundary through heuristics for angle selection, in lieu of uniformly-spaced angles from its maximum likelihood estimator. Two heuristics are given: an elliptic-inspired angle selection heuristic and an intelligent confidence region smoothing search heuristic. Each improves graphic quality and computation time over the established technique, and are automated in R with publicly available code via the Comprehensive R Archive Network conf() package.