A hidden renewal model for monitoring aquatic systems biosensors

This article proposes a method to model signals of oysters’ openings over time using a four‐state renewal process. Two of them are of particular interest and correspond to instants when the animals are open or closed. An estimator of the cumulative jump rate of the renewal process is provided. It relies on observations of the jumps between the four states. Here, these measures are not available, but the observed signal is assumed to take ranges of real values according to this underlying process. A procedure to estimate a probability density function that summarizes the information of the signal is explained. This leads to estimation of the hidden renewal process and of its cumulative jump rate for each oyster. We propose to classify these estimated functions for a group of oysters in order to discriminate these animals according to their health status. Such a diagnosis is essential when using these animals as biosensors for water quality assessment. Copyright © 2014 John Wiley & Sons, Ltd.