Marked regularity models

摘要

We present a generalization of the regularity model, which is anstationary point process model describing how often and how regularly anrandom “event” occurs. The generalization allows thenamplitude of each event to be a sample from a random process. First, wendeveloped closed-form approximations of the power spectra of datansegments; then we examined the accuracy of a procedure that estimatesnthe regularity and mark process parameters by minimizing the errornbetween measured spectra and the approximations. We found the following.nIn the absence of measurement noise, joint estimation of both mark andnregularity parameters is accurate only if the ratio of the square of thenmean of the marks to the variance of the marks (the SMNPR) is small.nMarginal estimation of the regularity process parameters can be accuratenif the mark process is taken into account by minimizing overallnparameters; the accuracy then depends on both measurement noise andnSMNPR. Error in the marginal estimation of the regularity processnparameters will be inversely proportional to the SMNPR if the marks arenignored by minimizing only with respect to the regularity parameters, sonignoring the marks can cause a substantial degradation in accuracy whennthe SMNPR is small. We illustrate these findings with an acousticnscattering example in which simulated ultrasound measurements of tissuensamples are characterized by their description in the parameter space