Non-linear compartmental systems: extensions of S. R. Bernard's urn model

One of the limitations of stochastic, linear compartmental systems is the small degree of variability in the contents of compartments. S. R. Bernard's (1981) urn model (S. R. Bernardet al., Bull. math. Biol. 43, 33–45.) which allows for bulk arrivals and departures from a one-compartment system, was suggested as a way of increasing content variability. In this paper, we show how the probability distribution of the contents of an urn model may be simply derived by studying an appropriate set of exchangeable random variables. In addition, we show how further increases in variability may be modeled by allowing the size of arrivals and departures to be random. Supported by NSF Grant No. MCS 8102215-01.