2003 | OriginalPaper | Buchkapitel
Sequential Bayes Detection of Trend Changes
verfasst von : Martin Beibel, Hans R. Lerche
Erschienen in: Foundations of Statistical Inference
Verlag: Physica-Verlag HD
Enthalten in: Professional Book Archive
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Let W t (0 ≤ t < ∞) denote a Brownian motion process which has zero drift during the time interval [0, v) and drift θ during the time interval [v, ∞), where θ and v are unknown. The process W is observed sequentially. The general goal is to find a stopping time T of W that ‘detects’ the unknown time point v as soon and as reliably as possible on the basis of this information. We work in a Bayesian framework and discuss a loss structure that is closely connected to that of the Bayes tests of power one of Lerche ([4]). This work extends Beibel’s ([2]) where only normal priors on θ were studied. An important ingredient in our proof is the comparison of the process of the posterior variance under different priors similar to the arguments in Paulsen ([6]).