Model processes in nonlinear prediction with application to detection and alarm
Lindgren, Georg LU
(1980)
In Annals of Probability
8(4).
p.775-792
- Abstract
- A level crossing predictor is a predictor process $Y(t)$, possibly multivariate, which can be used to predict whether a specified process $X(t)$ will cross a predetermined level or not. A natural criterion on how good a predictor is, can be the probability that a crossing is detected a sufficient time ahead, and the number of times the predictor makes a false alarm. If $X$ is Gaussian and the process $Y$ is designed to detect only level crossings, one is led to consider a multivariate predictor process $Y(t)$ such that a level crossing is predicted for $X(t)$ if $Y(t)$ enters some nonlinear region in $R^p$. In the present paper we develop the probabilistic methods for evaluation of such an alarm system. The basic tool is a model for the... (More)
- A level crossing predictor is a predictor process $Y(t)$, possibly multivariate, which can be used to predict whether a specified process $X(t)$ will cross a predetermined level or not. A natural criterion on how good a predictor is, can be the probability that a crossing is detected a sufficient time ahead, and the number of times the predictor makes a false alarm. If $X$ is Gaussian and the process $Y$ is designed to detect only level crossings, one is led to consider a multivariate predictor process $Y(t)$ such that a level crossing is predicted for $X(t)$ if $Y(t)$ enters some nonlinear region in $R^p$. In the present paper we develop the probabilistic methods for evaluation of such an alarm system. The basic tool is a model for the behavior of $X(t)$ near the points where $Y(t)$ enters the alarm region. This model includes the joint distribution of location and direction of $Y(t)$ at the crossing points. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1273172
- author
- Lindgren, Georg
LU
- organization
- publishing date
- 1980
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Annals of Probability
- volume
- 8
- issue
- 4
- pages
- 775 - 792
- publisher
- Institute of Mathematical Statistics
- ISSN
- 0091-1798
- language
- English
- LU publication?
- yes
- id
- f7040da0-40c6-422e-ae2a-d3b4c4ad2954 (old id 1273172)
- alternative location
- http://www.jstor.org/stable/2242825?origin=JSTOR-pdf
- date added to LUP
- 2016-04-04 09:18:23
- date last changed
- 2019-03-08 03:04:18
@article{f7040da0-40c6-422e-ae2a-d3b4c4ad2954,
abstract = {{A level crossing predictor is a predictor process $Y(t)$, possibly multivariate, which can be used to predict whether a specified process $X(t)$ will cross a predetermined level or not. A natural criterion on how good a predictor is, can be the probability that a crossing is detected a sufficient time ahead, and the number of times the predictor makes a false alarm. If $X$ is Gaussian and the process $Y$ is designed to detect only level crossings, one is led to consider a multivariate predictor process $Y(t)$ such that a level crossing is predicted for $X(t)$ if $Y(t)$ enters some nonlinear region in $R^p$. In the present paper we develop the probabilistic methods for evaluation of such an alarm system. The basic tool is a model for the behavior of $X(t)$ near the points where $Y(t)$ enters the alarm region. This model includes the joint distribution of location and direction of $Y(t)$ at the crossing points.}},
author = {{Lindgren, Georg}},
issn = {{0091-1798}},
language = {{eng}},
number = {{4}},
pages = {{775--792}},
publisher = {{Institute of Mathematical Statistics}},
series = {{Annals of Probability}},
title = {{Model processes in nonlinear prediction with application to detection and alarm}},
url = {{http://www.jstor.org/stable/2242825?origin=JSTOR-pdf}},
volume = {{8}},
year = {{1980}},
}