A Bayesian Change-Point Problem with an Application to the Prediction and Detection of Ovulation in Women

Abstract

Under the assumptions of independent normally distributed and sequentially observed responses, a Bayesian rule for detecting a change from a constant mean response is derived. It is known that both basal body temperature (BBT) and preovulatory estrogen values undergo such a change in mean value at some random time during the menstrual cycle. The Bayesian rule is applied to estrogen to predict ovulation and to BBT to detect ovulation. Data from an aggregate of women are used to obtain prior information about the change-points and the parameters that define the changes in estrogen and BBT. A method is proposed by which the accumulation of information for a specific women can be incorporated into the aggregate prior information.