Large deviations for template matching between point processes
| dc.creator | Chi, Zhiyi | |
| dc.date | 2005-03-22 | |
| dc.date.accessioned | 2026-07-07T05:18:13Z | |
| dc.date.available | 2026-07-07T05:18:13Z | |
| dc.description | We study the asymptotics related to the following matching criteria for two independent realizations of point processes X\sim X and Y\sim Y. Given l>0, X\cap [0,l) serves as a template. For each t>0, the matching score between the template and Y\cap [t,t+l) is a weighted sum of the Euclidean distances from y-t to the template over all y\in Y\cap [t,t+l). The template matching criteria are used in neuroscience to detect neural activity with certain patterns. We first consider W_l(θ), the waiting time until the matching score is above a given threshold θ. We show that whether the score is scalar- or vector-valued, (1/l)\log W_l(θ) converges almost surely to a constant whose explicit form is available, when X is a stationary ergodic process and Y is a homogeneous Poisson point process. Second, as l\to\infty, a strong approximation for -\log [\Pr{W_l(θ)=0}] by its rate function is established, and in the case where X is sufficiently mixing, the rates, after being centered and normalized by \sqrtl, satisfy a central limit theorem and almost sure invariance principle. The explicit form of the variance of the normal distribution is given for the case where X is a homogeneous Poisson process as well. | |
| dc.description | Published at http://dx.doi.org/10.1214/105051604000000576 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0503463 | |
| dc.identifier | http://arxiv.org/abs/math/0503463 | |
| dc.identifier | Annals of Applied Probability 2005, Vol. 15, No. 1A, 153-174 | |
| dc.identifier | doi:10.1214/105051604000000576 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74587 | |
| dc.subject | Probability | |
| dc.subject | 60F10 (Primary) 60G55 (Secondary) | |
| dc.title | Large deviations for template matching between point processes | |
| dc.type | text |