Some Topics in Computer Assisted Modeling, Simulation, and Data Analysis
Final rept. 1 Aug 1999-31 Jul 2002
RICE UNIV HOUSTON TX DEPT OF STATISTICS
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The supported graduate student, John Dobelman has begun extensive work on his disseration to find stochastic models to explain the mechanisms whereby electricity prices spike. Three books and six papers were authored or co-authored by Thompson during this grant period. The common thread is the development of models supported by intensive computer simulation to help explain and understand real world processes. Among these investigations are included models for statistical process control in situations new to SPC. Almost all SPC treatises deal with situations in which the paradigm is of mature usage. Thompson shows how difficult such implementations are to achieve in practice and gives means for jumpstarting SPC in such systems as the International Space Station. The first world AIDS epidemic has received substantial attention by Thompson. Most recently he has given a model based argument that there is no standalone AIDS epidemic in Europe it only exists by contacts with American infectives. In stochastic process based economic modeling, Thompson and his co-authors have shown how effective simulation models of relative simplicity and parametric parsimony may be achieved by aggregation from the micro to the macro. The simugram is Thompsons discovery that we can forecast the future multivariate stochastic process of even a large portfolio by the use of simulation. The risk neutral formula of Black-Scholes-Merton is shown to be seriously deficient as a practical tool. Similarly, the artificiality of the portfolio paradigm of Markowitz is replaced by other, conceptually simple, but requiring extensive computer simulation, techniques. Work is done which shows how data analysis in high dimensions needs to be carried out with techniques very different from those used in low dimensions.
- Numerical Mathematics
- Statistics and Probability