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Estimating arrival rate of nonhomogeneous Poisson processes with semidefinite programming

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  • Farid Alizadeh
  • David Papp

Abstract

We present a summary of methods based on semidefinite programming for estimating arrival rate of nonhomogeneous Poisson processes from a finite set of observed data. Both one-dimensional time dependent, and multi-dimensional time and location dependent rates are considered. The arrival rate is a nonnegative function of time (or time and location). We also assume that it is a smooth function with continuous derivatives of up to certain order k. We estimate the rate function by one or multi-dimensional splines, with the additional condition that the underlying rate function is nonnegative. This approach results in an optimization problem over nonnegative polynomials, which can be modeled and solved using semidefinite programming. We also describe a method which requires only linear constraints. Numerical results based on e-mail arrival and highway accidents are presented. Copyright Springer Science+Business Media, LLC 2013

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  • Farid Alizadeh & David Papp, 2013. "Estimating arrival rate of nonhomogeneous Poisson processes with semidefinite programming," Annals of Operations Research, Springer, vol. 208(1), pages 291-308, September.
    • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:p:291-308:10.1007/s10479-011-1020-2
    DOI: 10.1007/s10479-011-1020-2
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    1. NESTEROV, Yu., 2000. "Squared functional systems and optimization problems," LIDAM Reprints CORE 1472, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Farid Alizadeh & Jonathan Eckstein & Nilay Noyan & Gábor Rudolf, 2008. "Arrival Rate Approximation by Nonnegative Cubic Splines," Operations Research, INFORMS, vol. 56(1), pages 140-156, February.
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