Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

Summary. Seeds are planted on the interval [0, L] at various locations. Each seed has a location x and a potential germination time tε [0, ∞), and it is assumed that the collection of such (x, t) pairs forms a Poisson process in [0, L] × [0, ∞) with intensity measure dxdΛ(t). From each seed that germinates, an inhibiting region grows bidirectionally at rate 2v.These regions inhibit germination of any seed in the region with a later potential germination time. Thus, seeds only germinate in the uninhibited part of [0, L]. We want to estimate Λ on the basis of one or more realizations of the process, the data being the locations and germination times of the germinated seeds. We derive the maximum likelihood estimator of v and a nonparametric estimator of Λ and describe methods of obtaining parametric estimates from it, illustrating these with reference to gamma densities. Simulation results are described and the methods applied to some neurobiological data. An Appendix outlines the S-PLUS code used.

Keywords

Boolean model, DNA replication, Germination-growth process, Inhibition, Maximum likeli-hood estimation, Nucleation, Synaptic transmission

Publication Date

9-2000

Source Publication Title

Biometrics

Volume

56

Issue

3

Start Page

755

End Page

760

Publisher

Wiley

Peer Reviewed

1

Copyright

This is the peer reviewed version of the following article: Chiu, S., Quine, M., & Stewart, M. (2000). Nonparametric and Parametric Estimation for a Linear Germination-Growth Model. Biometrics, 56(3), 755-760. Retrieved from http://www.jstor.org/stable/2676918, which has been published in final form at https://dx.doi.org/10.1111/j.0006-341X.2000.00755.x. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

Funder

This research was supported by an FRG grant of the Hong Kong Baptist University and by the Australian Research Council.

DOI

10.1111/j.0006-341X.2000.00755.x

ISSN (print)

0006341X

ISSN (electronic)

15410420

Additional Files

JA-4887-29104_suppl.txt (33 kB)

Included in

Mathematics Commons

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