Estimating arrival rate of nonhomogeneous Poisson processes with semidefinite programming

Farid Alizadeh, David Papp

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)291-308
Number of pages18
JournalAnnals of Operations Research
Issue number1
StatePublished - Sep 2013

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research


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