A dynamic change-point model for detecting the onset of growth of bacteriological infections

We consider a structural component model based on a random walk that incorporates a drift from an unknown point in time, τ, with the objective of providing an on‐line estimate of this changepoint. The application to detecting bacteriological growth in routine monitoring of feedstuff motivates the analysis, and the ability of this model to be tuned in different ways for different specific applications is the reason for its choice. The changepoint τ is regarded as a parameter and the posterior distribution (or likelihood function) of τ is computed at each time point by running a triangular multiprocess Kalman filter. The values of other parameters in the structural component model are tuned from previous data. The location and width of an 80% posterior interval give both an estimate of the changepoint and the magnitude of the evidence for a change. A more formal decision rule for on‐line and post‐sampling detection is derived by application of Bayesian decision analysis.