BAYESIAN-APPROACH FOR BOD AND DO WHEN THE DISCHARGED POLLUTANTS ARE RANDOM

A stochastic model for biochemical oxygen demand (BOD) and disserved o xygen (DO) at a distance t downstream, when pollutants are discharged over a continuous stretch, is a random differential equation of the fo rm X(t) = AX(t) + Y(t), t greater than or equal to O, with the initial condition X(O)= X(O). Assuming that X(O) is a random vector having a bivariate normal distribution with the mean vector mu(O) and the preci sion (the inverse of the variance-covariance) matrix Lambda(O), we pro vide the prediction equation ($) over cap X(t) at any point t by emplo ying (i) a normal prior for mu(O) keeping Lambda(O) fixed and known, a nd (ii) a normal-Wishart prior for (mu(O), Lambda(O)). The theory is s upplemented by numerical studies.