A Bayesian Approach to Sequential Surveillance in Exponential Families

Abstract

We describe herein a Bayesian change-point model and the associated recursive formulas for the estimated time-varying parameters and the posterior probability that a change-point has occurred at a particular time. The proposed model is a variant of that of Chernoff and Zacks (1964) for the case of normal means with known common variance. It considers more generally the multiparameter exponential family and addresses the complex statistical issues due to multiple change-points and unknown pre- and post-change system parameters in sequential surveillance. A sequential detection rule based on the proposed model is also introduced and its false alarm rate and mean detection delay are studied in the multiple change-point setting.

Keywords:

• Accumulated prediction error
• Bounded complexity mixture
• Detection delay
• False alarm
• Filtering
• Segmentation

Mathematics Subject Classification:

• Primary 62L15
• Secondary 62G40