A Haar-Fisz algorithm for Poisson intensity estimation

PZ Fryzlewicz, GP Nason

Research output: Contribution to journalArticle (Academic Journal)peer-review

134 Citations (Scopus)


This article introduces a new method for the estimation of the intensity of an inhomogeneous one-dimensional Poisson process. The Haar-Fisz transformation transforms a vector of binned Poisson counts to approximate normality with variance one. Hence we can use any suitable Gaussian wavelet shrinkage method to estimate the Poisson intensity. Since the Haar-Fisz operator does not commute with the shift operator we can dramatically improve accuracy by always cycle spinning before the Haar-Fisz transform as well as optionally after. Extensive simulations show that our approach usually significantly outperformed state-of-the-art competitors but was occasionally comparable. Our method is fast, simple, automatic, and easy to code. Our technique is applied to the estimation of the intensity of earthquakes in northern California. We show that our technique gives visually similar results to the current state-of-the-art.
Translated title of the contributionA Haar-Fisz algorithm for Poisson intensity estimation
Original languageEnglish
Pages (from-to)621 - 638
Number of pages18
JournalJournal of Computational and Graphical Statistics
Volume13 (3)
Publication statusPublished - 1 Sept 2004

Bibliographical note

Publisher: American Statistical Association
Other identifier: IDS Number: 846CI


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