Visualization and Diagnostics of Nonlinear Statistical Models
College: Liberal Arts and Sciences
Award year: 2002-2003
Nonlinear statistical models arise in many areas of research in a wide range of disciplines. The least squares principle is used to estimate the parameters in nonlinear models and iterative numerical methods are used to find the set of parameters that minimize the residual sum of squares surface. Nonlinear least squares regression problems are intrinsically hard, and it is generally possible to find a dataset that will defeat even the most robust numerical codes.
The objective of this proposal is to integrate diagnostics of nonlinear regression fitting procedures and visualization of multidimensional parameter spaces to create an innovative graphics environment that will educate and provide insight for scientists from all disciplines that fit nonlinear models and/or interpret their results. The proposed activities are as follows:
- Visualization of the residual sum of squares surface. This activity will involve the construction of contour and perspective plots with the appropriate slicing and projection of the multidimensional parameter space to provide insight into the location and function value of local minimum of the residual sum of squares surface. This activity also involves the development of a dynamic diagnostic tool which would allow the user to take a visual tour of the surface.
- Graphical display and visualization of likelihood based inference of model parameters. This activity will involve contouring or color coding the sets of parameters that are not significantly (at some specified confidence level) different from the least squares estimate on the residual sum of squares surface.
- Diagnostics for visualization. This activity will involve quantifying the uncertainty of a three dimensional image in visualization and virtual environments at the pixel level and integrate that information into the image.