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On Updating Algorithms and Inference for Stochastic Point Processes

Published online by Cambridge University Press:  05 September 2017

D. Vere-Jones
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Abstract

This paper is an attempt to interpret and extend, in a more statistical setting, techniques developed by D. L. Snyder and others for estimation and filtering for doubly stochastic point processes. The approach is similar to the Kalman-Bucy approach in that the updating algorithms can be derived from a Bayesian argument, and lead ultimately to equations which are similar to those occurring in stochastic approximation theory. In this paper the estimates are derived from a general updating formula valid for any point process. It is shown that almost identical formulae arise from updating the maximum likelihood estimates, and on this basis it is suggested that in practical situations the sequence of estimates will be consistent and asymptotically efficient. Specific algorithms are derived for estimating the parameters in a doubly stochastic process in which the rate alternates between two levels.

Type
Part VI — Statistical Inference on Stochastic Processes
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 239 - 259
Copyright
Copyright © 1975 Applied Probability Trust 

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