Integral estimation based on Markovian design

Romain Azaïs 1, 2 Bernard Delyon 3 François Portier 4
1 BIGS - Biology, genetics and statistics
Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
4 Groupe STA Statistiques et applications [Paris]
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : 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.
Type de document :
Article dans une revue
Advances in Applied Probability, Applied Probability Trust, In press
Liste complète des métadonnées

Littérature citée [27 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01360647
Contributeur : Romain Azaïs <>
Soumis le : mercredi 4 octobre 2017 - 14:44:51
Dernière modification le : mardi 24 juillet 2018 - 01:13:06

Fichier

accel7.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Romain Azaïs, Bernard Delyon, François Portier. Integral estimation based on Markovian design. Advances in Applied Probability, Applied Probability Trust, In press. 〈hal-01360647v2〉

Partager

Métriques

Consultations de la notice

231

Téléchargements de fichiers

27