Some Topics in Data Analysis and Stochastic Modeling

The advent of high speed computing on the PC provides new possibilities for data based modeling. One key is simulation. Simulation gives us a venue for dealing with parameter estimation in stochastic models not previously tractable. We consider examples from oncology, economics, statistical process control and epidemiology. We essentially consider two realities, the first consisting of random nonparametric interpolations of the data and the second random implementations based on a mathematical model. We use simulation to change the model parameters to bring the reality of the model to consistency with that of the data. Also, high speed computing enables us to carry out nonparametric data analysis in higher dimensions. The key here is to build algebraic rather than geometrical algorithms. We show how nonparametric data analysis in high dimensions say greater than three should generally not be treated as one of nonparametric density estimation but rather should start with finding centers of relatively high density and then use parametric approximations in the neighborhoods of these modes.