Bayesian prediction in doubly stochastic Poisson process

Alicja Jokiel-Rokita, Daniel Lazar and Ryszard Magiera ()

Metrika: International Journal for Theoretical and Applied Statistics, 2014, vol. 77, issue 8, 1023-1039

Abstract: A stochastic marked point process model based on doubly stochastic Poisson process is considered in the problem of prediction for the total size of future marks in a given period, given the history of the process. The underlying marked point process $$(T_{i},Y_{i})_{i\ge 1}$$ ( T i , Y i ) i ≥ 1 , where $$T_{i}$$ T i is the time of occurrence of the $$i$$ i th event and the mark $$Y_{i}$$ Y i is its characteristic (size), is supposed to be a non-homogeneous Poisson process on $$\mathbb {R}_{+}^{2}$$ R + 2 with intensity measure $$P\times \varTheta $$ P × Θ , where $$P$$ P is known, whereas $$\varTheta $$ Θ is treated as an unknown measure of the total size of future marks in a given period. In the problem of prediction considered, a Bayesian approach is used assuming that $$\varTheta $$ Θ is random with prior distribution presented by a gamma process. The best predictor with respect to this prior distribution is constructed under a precautionary loss function. A simulation study for comparing the behavior of the predictors under various criteria is provided. Copyright The Author(s) 2014

Keywords: Bayes prediction; Doubly stochastic Poisson process; Random measure; Precautionary loss (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:77:y:2014:i:8:p:1023-1039

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DOI: 10.1007/s00184-014-0484-x

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