Visualize uncertainty

These figures are examples from my research on how uncertainty can be visualized. Most of the figures show constraints on values that a process can take. Some of the examples are taken from my doctoral dissertation.

Non-linear mapping of uncertainty through a function

For a nonlinear function how uncertainty is mapped depends on the specific range of values. The mapping of uncertainty is demonstrated by taking uniform samples of the input range. This figure was created using a program that generates PostScript code.

Global bounds on a function

The plot shows how different ranges of the input parameter led to varying global bounds on the value that a function can take. This figure was created using a program that generates PostScript code.

Two time series under uncertainty

This figure shows how uncertainty in abundance increases over time for two different models of population growth. This figure was created using a program that generates PostScript code.

Bounds on an iterative growth process

This figure demonstrates how uncertainty in the ouput of a model can grow in time given initial uncertainty in the parameters. The inner lines are from uniform samples of the parameter and initial conditon. They show that Monte Carlo methods are not always effective in finding the minimum and/or maximum of a complicated function. The figure was created using a program that generates PostScript code.

A parametric solution set

The figure is of a solution set for a linear equation and a feasible data set. The solution set is composed entirely of rectangles. The figure shows how the SIVIA algorithm conservatively bounds the solution set. This figure was created using a program that generates PostScript code.

Demonstration of a mathematical transformation

This figure was created in PostScript and demonstrates how two quadratic forms can be jointly diagonalized. The form on the left is an ellipse and the form on the right is a hyperbola. Each letter represents a different step in the joint transformation. The figure uses PostScript's geometric scaling, rotation, and translation to do the mathematics.