Marked regularity models

We present a generalization of the regularity model, which is a stationary point process model describing how often and how regularly a random "event" occurs. The generalization allows the amplitude of each event to be a samp le from a random process. First, we developed closed-form approximations of the power spectra of data segments, then we examined the accuracy of a pro cedure that estimates the regularity and mark process parameters by minimiz ing the error between measured spectra and the approximations. We found the following. In the absence of measurement noise, joint estimation of both m ark and regularity parameters is accurate only if the ratio of the square o f the mean of the marks to the variance of the marks (the SMNPR) is small. Marginal estimation of the regularity process parameters can be accurate if the mark process is taken into account by minimizing over all parameters; the accuracy then depends on both measurement noise and SMNPR. Error in the marginal estimation of the regularity process parameters will be inversely proportional to the SMNPR if the marks are ignored by minimizing only with respect to the regularity parameters, so ignoring the marks can cause a su bstantial degradation in accuracy when the SMNPR is small. We illustrate th ese findings with an acoustic scattering example in which simulated ultraso und measurements of tissue samples are characterized by their description i n the parameter space.