Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Statistics and Actuarial Sciences


Dr. W. John Braun


Point process data with a latent or hidden component arise in a variety of research fields. Examples include reaction time, forest fires, seismology, and transactional data. We develop statistical methodology that can be applied to point process data with a latent component. The methodology is applied to data from a number of reaction time (RT) experiments. Reaction time experiments have been of interest to psychophysicists for more than a century. A reason for this interest lies in the fact that the time taken to perform a task indicates the complexity of the operations occurring in the brain. We study three types of visual-motor RT experiments that increase in complexity. The main contributions of my thesis are the development of two types of models that can be used in the analysis of point process data, in particular RT data. For each of the three RT experiments, we develop a parametric model to help provide a foundation for understanding the behavior of nonparametric intensity estimates. We also study threshold models and introduce different variants for the three RT experiments. The parameters in a threshold model have direct biological interpretations regarding inferences on the eye-brain-hand system. Additional contributions include the use of nonlinear regression in parameter esti111 mation for our simple RT parametric model. This estimation method is useful when it is of interest to obtain a single set of parameter estimates for data sets obtained using different flash rates. We also provide a derivation of a covariance that is necessary for a hypothesis test by Asimit and Braun (2005).



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