Mathematical Sciences: Interactive Display and Exploration of Likelihood Surfaces

本研究旨在为似然曲面或后验密度曲面的交互式图形显示和探索提供理论和先进的计算方法。在统计推断的似然方法和贝叶斯方法中，表示数据集的统计模型中合理参数值的区域由参数函数的等高线限定。本研究旨在开发和改进一种使用来自目标函数轮廓的信息来显示此类等高线的二维投影的方法。我们的目标是制造一种检查似然曲面和后验密度曲面的工具，以取代现在所做的对可能不准确的数值汇总的依赖。这项研究属于图形统计的发展中的学科。其他人正试图通过提高数值积分能力来扩大贝叶斯统计的适用性。这项建议采取了一种不同的方法，建议通过开发图形解决方案来绕过数值困难。

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.