A DYNAMIC CHANGE-POINT MODEL FOR DETECTING THE ONSET OF GROWTH IN BACTERIOLOGICAL INFECTIONS

We consider a structural component model based on a random walk that i ncorporates a drift from an unknown point in time, tau, with the objec tive of providing an on-line estimate of this changepoint. The applica tion to detecting bacteriological growth in routine monitoring of feed stuff motivates the analysis, and the ability of this model to be tune d in different ways for different specific applications is the reason for its choice. The changepoint tau is regarded as a parameter and the posterior distribution (or likelihood function) of tau is computed at each time point by running a triangular multiprocess Kalman filter. T he values of other parameters in the structural component model are tu ned from previous data. The location and width of an 80% posterior int erval give both an estimate of the changepoint and the magnitude of th e evidence for a change. A more formal decision rule for on-line and p ost-sampling detection is derived by application of Bayesian decision analysis.