Johnson, Don H.2018-12-182018-12-181980Swami, Ananthram. "Estimation techniques in non-stationary renewal processes." (1980) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/104494">https://hdl.handle.net/1911/104494</a>.https://hdl.handle.net/1911/104494The multiplicative intensity model for the intensity function u(t;N(t);w) = v(t)r(t - of a self-exciting point process is analyzed in terms of the distortion of v(t) by the channel r(x). A convenient and common method of presenting point process data, the Post Stimulus Histogram is shown to be related to the ensemble average of the intensity process and hence incorporates stimulus v() as well as refractory r() related effects. This quantity is not usually amenable to closed-form representation. We propose an approximation to the PST which is reasonably good under specified conditions. A maximum likelihood estimator of r(x), where v(t) is known, is derived. A maximum likelihood estimator of v(t), given r(x), is also derived. This estimator is meaningful only when the signal v(t) is known to be periodic. The M.L. Estimator compensates for relative dead-time effects. We propose an iterative dead-time processor, which operating on the histogram obtained from the M.L. Estimate, partially compensates for absolute dead-time effects. The performance of these estimators is compared with those of other procedures. Applications to spike trains recorded from auditory neurons are discussed.110 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.ThesisRICE2129reformatted digitalTHESIS E.E. 1980 SWAMI