Mathematical Sciences: Interactive Display and Exploration of Likelihood Surfaces

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This research is to provide theoretical and advanced computational methods for the interactive graphical display and exploration of likelihood surfaces or posterior density surfaces. In both the likelihood and Bayesian methods of statistical inference, the regions which represent reasonable parameter values in a statistical model for a data set are bounded by contours of a function of parameters. This research aims to develop and enhance a method of displaying two-dimensional projections of such contours using information from the profile of the objective function. The goal is produce a tool for examining likelihood surfaces and posterior density surfaces that replaces the reliance on possibly inaccurate numerical summaries as is done now. This research is in the developing discipline of graphical statistics. Others are trying to extend the applicability of Bayesian statistics by improving numerical integration capabilities. This proposal takes a different approach which proposes to bypass the numerical difficulties by developing graphical solutions instead.