Effective modeling and scientific computation with applications to health study, astronomy, and queueing network

This dissertation presents statistics and probability modeling and computation applied to three areas: (I) health study, (II) astronomy, and (III) queueing network, for which the modeling strategies and computation techniques cover a broad range. I. National Latino and Asian American Study (NLAAS) is the most recent large-scale psychiatric epidemiologic survey, with an embedded experiment comparing different question forms. Serious underreporting was detected due to different question orders received by respondents. Our object is to reduce and correct such response bias due to survey instrument. We address such a problem and created multiply imputed data sets for public use. II. NASA's Gravity Probe B is the most recent experimental study on the general theory of relativity. As part of the mission, the motion of the guide star of GP-B needed to be measured independently. We use Bayesian methods and a linear model with complex variance structures to estimate the proper motion of the star and study the effects of various assumptions involving the parameters of a both the physical model and the measurement model on our final estimates. III. We develop a strongly efficient rare-event simulation algorithm for computing the tail probabilities of the steady-state waiting time in a single server queue with regularly varying service times. Our approach takes advantage of the regenerative ratio formula for the steady-state distribution, and it does not use the first passage time representation that is particular to the delay in the G / G /1 queue. Hence, the strategy has the potential to be applied in more general queueing models.