Eyeball Parameter Estimation with a Computer

Great promise is shown by combining man and computers via interactive graphics to solve problems neither could solve alone. The behavior of man in this problem-solving combination must be studied just as any computer problem-solving system. The example problem studied is parameter estimation. After collecting observational data, a mathematical model of the data generation process is constructed which generates predicted data which varies according to some parameters of the model. The problem is to find parameters which ``fit´´ predicted data to collected data. Three methods are typically used to solve this problem: calculate parameters as a function of the observational data, ``grid search´´ the parameter space, and ``hill climb´´ in the parameter space. In all these procedures, ``feel´´ of the data and model are lost. Systematic differences may be present which suggest data collection errors or a need to reformulate the model. An interactive graphics curve-fitting procedure has been developed which both fits curves and gives the man some feel of the process. Collected data are displayed. The man then iteratively enters trial parameters and immediately observes the predicted data along with the collected data (and other predicted data curves). Collected data for problems with two parameters were generated using linear, sinusoidal, exponential, and logrithmic models to which random error and sometimes systematic error components were added. Collected data for problems with four parameters were generated using a model of short-term memory and random error.