Optimal experimental designs for stochastic processes whose covariance is a function of the mean
Seminar Room 1, Newton Institute
Recent literature emphasizes, for the analysis of compartmental models, the need for models for stochastic processes whose covariance structure depends on the mean. Covariance functions must be positive definite and this fact is nontrivial and constitutes one of the challenges of the present work, for a stochastic process whose covariance is a function of the mean. We show that there exists a class of functions that, composed with the mean of the process, preserve positive definiteness and can be used for the purposes of the present talk. We offer some examples for an easy construction of such covariances and then study the problem of locally D-optimal design through both simulation studies as well as real data inherent to a radiation retention model in the human body.