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.
@article{1176345076,
author = {Novic, Bradley},
title = {Bayes Sequential Estimation of a Poisson Rate: A Discrete Time Approach},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 840-844},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345076}
}
Novic, Bradley. Bayes Sequential Estimation of a Poisson Rate: A Discrete Time Approach. Ann. Statist., Tome 8 (1980) no. 1, pp. 840-844. http://gdmltest.u-ga.fr/item/1176345076/