Bernoulli

  • Bernoulli
  • Volume 24, Number 4B (2018), 3628-3656.

Detecting Markov random fields hidden in white noise

Ery Arias-Castro, Sébastien Bubeck, Gábor Lugosi, and Nicolas Verzelen

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Abstract

Motivated by change point problems in time series and the detection of textured objects in images, we consider the problem of detecting a piece of a Gaussian Markov random field hidden in white Gaussian noise. We derive minimax lower bounds and propose near-optimal tests.

Article information

Source
Bernoulli, Volume 24, Number 4B (2018), 3628-3656.

Dates
Received: February 2016
Revised: December 2016
First available in Project Euclid: 18 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1524038765

Digital Object Identifier
doi:10.3150/17-BEJ973

Mathematical Reviews number (MathSciNet)
MR3788184

Zentralblatt MATH identifier
06869887

Keywords
Markov random fields detection combinatorial testing minimax test image analysis

Citation

Arias-Castro, Ery; Bubeck, Sébastien; Lugosi, Gábor; Verzelen, Nicolas. Detecting Markov random fields hidden in white noise. Bernoulli 24 (2018), no. 4B, 3628--3656. doi:10.3150/17-BEJ973. https://projecteuclid.org/euclid.bj/1524038765


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Supplemental materials

  • Supplement to “Detecting Markov random fields hidden in white noise”. This supplement contains the remaining proofs.