Bayesian multiple curve fitting in the analysis of neuronal data

In this thesis, the method of Bayesian Adaptive Regression Splines (BARS) is used and extended to fit many similar functions non-parametrically. Special attention is given to Poisson process intensity functions, which are used to model neuronal firing rates.; Many neurophysiological studies obtain data from hundreds of neurons and attempt to describe the regularity and variability among them. We addressed this subject by implementing multiple curve-fitting, or modeling a group of neurons, and also through the application of Bayesian functional data analysis. Variants of approaches to multiple curve-fitting are discussed. The emphasis has been put on the calculation of the between-curve variability while keeping track of the uncertainty within curves, which may result from recording the neuronal activity in a relatively small number of trials.; Various applications of statistical techniques in conjunction with multiple curve-fitting are discussed. Included is the method of curve registration for the alignment of curves fitted to neuronal firing activities.; Also, the technique of model-based clustering is modified so that not only are neurons classified based on the patterns of their firing rates, but the uncertainty due to the estimation of each curve is also accounted for. The method is illustrated by its ability to detect and describe the activity of a group of muscle-like neurons during the performance of experimental tasks that require the involvement of multi-joint muscle movements.; This thesis also includes a method for screening neurons. The screening technique would enable the investigator to screen out those neurons whose firing patterns do not discriminate between two experimental tasks.