Inference for Stationary Random Fields given Poisson Samples.

Abstract

This paper examines some questions of statistical inference -- specifically, estimation of the mean and covariance function, as well as linear state estimation -- for stationary random fields observable only at the points of a (likewise) Poisson process. Given a d-dimensional random field and a Poisson process independent of it, suppose that it is possible to observe only the location of each point of the Poisson process and the value of the random field at that (randomly located) point. Nonparametric estimators of the mean and covariance function of the random field - based on observation over compact sets of single realizations of the Poisson samples - are constructed. Under fairly mild conditions these estimators are consistent (in various senses) as the set of observation becomes unbounded in a suitable manner. The state estimation problem of minimum mean squares reconstruction of unobserved values of the random field is also examined.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1985
Accession Number
ADA160191

Entities

People

  • A. F. Karr

Organizations

  • Johns Hopkins University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Acquisition
  • Algorithms
  • Availability
  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Mathematical Analysis
  • Mathematics
  • Observation
  • Security
  • Stationary
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Plasma Physics / Magnetohydrodynamics
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms