Integral estimation based on Markovian design - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Advances in Applied Probability Année : 2018

Integral estimation based on Markovian design

Résumé

Suppose that a mobile sensor describes a Markovian trajectory in the ambient space. At each time the sensor measures an attribute of interest, e.g., the temperature. Using only the location history of the sensor and the associated measurements, the aim is to estimate the average value of the attribute over the space. In contrast to classical probabilistic integration methods, e.g., Monte Carlo, the proposed approach does not require any knowledge on the distribution of the sensor trajectory. Probabilistic bounds on the convergence rates of the estimator are established. These rates are better than the traditional "root n"-rate, where n is the sample size, attached to other probabilistic integration methods. For finite sample sizes, the good behaviour of the procedure is demonstrated through simulations and an application to the evaluation of the average temperature of oceans is considered.
Fichier principal
Vignette du fichier
accel7.pdf (832.51 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01360647 , version 1 (06-09-2016)
hal-01360647 , version 2 (04-10-2017)

Identifiants

Citer

Romain Azaïs, Bernard Delyon, François Portier. Integral estimation based on Markovian design. Advances in Applied Probability, 2018, 50 (3), pp.833-857. ⟨10.1017/apr.2018.38⟩. ⟨hal-01360647v2⟩
371 Consultations
145 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More