Integrated marked Poisson processes with application to image correlation spectroscopy

Image correlation spectroscopy (ICS) is an experimental technique used in the study of cell tissue, specifically to obtain information about protein aggregates. This paper discusses a filtered Poisson process model of ICS, and uses this to obtain the sampling distribution of an estimator of interest, using spectral methods. Integrals of third- and fourth-order spectra are involved, and methods proposed in the literature are studied numerically. They are found to be infeasible methods, requiring months of computing time. An alternative method is proposed and is illustrated on some actual ICS experiments. A novel feature in this study is the use of a SIMD-class parallel computer, a MasPar MP-2 machine, to obtain some statistical properties of the estimation method.