Bayes Sequential Estimation of a Poisson Rate: A Discrete Time Approach
The Annals of Statistics · 1980 · Volume 8 · Issue 4
Abstract
This paper provides explicit solutions to the problem of estimating the arrival rate $\lambda$ of a Poisson process using a Bayes sequential approach. The loss associated with estimating $\lambda$ by $d$ is assumed to be of the form $(\lambda - d)^2\lambda^{-p}$ and the cost of observation includes both a time cost and an event cost. A discrete time approach is taken in which decisions are made at the end of time intervals having length $t$. Limits of the procedures as $t$ approaches zero are discussed and related to the continuous time Bayes sequential procedure.
Keywords
62C10, 62L12, 62L15, Bayes sequential estimation, Optimal stopping, Poisson process, sequential decision procedure
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