Mixture models of stochastic compartmental systems

Abstract

Stochastic compartmental models based on retention time distributions with random rate parameters are derived for the single compartment system and the two-compartment irreversible system. Often when the mixing distributions (i.e. the distributions of the rate parameter) are conjugate prior distributions for particular retention time distributions, the resulting mixture models (i.e. regression functions) are expressible in analytical forms. Many such mixture models are derived and the means and variances for the residence time random variable are also obtained. However in other cases, particularly when the mixing distributions are not conjugate priors, the models are expressible in integral forms only. A numerical procedure is suggested for fitting these integral forms to a data set. The application of the derived mixture models is illustrated with several data sets.