A Bayesian Approach to a Generalized House Selling Problem
The problem of choosing the one best or several best of a set of sequentially observed random variables has been treated by many authors. For example, the seller of a house has this problem when deciding which bids on the house to accept and which to reject. We assume that the bids are identically distributed random variables and at most n can be observed. Each bid is accepted or rejected when received; a bid rejected now cannot be accepted later on. The object is to maximize the expected value of the bid actually accepted. Unlike most previous authors, we examine the case where one or more parameters of the common underlying distribution are unknown and information on these is updated in a Bayesian manner as the successive random variables are observed. Using the properties of location and scale parameters, an explicit form for the optimal policy is found when the underlying distribution is normal, uniform, or gamma and the prior is from the natural conjugate family. Simulation results concerning sensitivity of the value obtained to the amount and correctness of the prior information for these three families is then presented.
Volume (Year): 24 (1977)
Issue (Month): 4 (December)
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