When is it best to follow the leader?

Quan Zhou, Department of Statistics, Rice University, USA

We study a classical continuous-time optimal scanning problem with N boxes. A missing object is hidden in one box according to a given prior probability distribution. The goal is to find out which box contains the object. When we search a box, we observe a signal evolving as a Brownian motion with a constant drift if the box contains the object, or as a Brownian motion with drift zero otherwise. This problem was first studied by Posner and Rumsey (1966), who conjectured that the optimal search strategy is to always observe the box with the largest posterior. However, we prove that this conjecture is not true in general and provide counterexamples for some specific prior distributions. But it remains open whether this strategy is optimal for the uniform prior distribution. Joint work with Philip Ernst and L.C.G. Rogers.

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