Zsolt Talata

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Project Euclid - mathematics and statistics online. Sequential change-point detection when unknown parameters are present in the pre-change distribution Yajun Mei; 92 - 122. Project Euclid - mathematics and statistics online. The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. Zsolt Talata Date defended: April 16, 2013. The Thesis Committee for Cody E. Clifton certi es that this is the approved version of the following thesis. Faculty mentor: Zsolt Talata, associate professor of mathematics. John (Jack) Johnston, senior in mathematics, economics and physics, Overland Park: “Initial-Boundary Value Problems for the Serre System,” a project on the unified transform method to analyze the linear component of the Serre system of water waves.

  • Volume 34, Number 1 (2006), 123-145.

Consistent estimation of the basic neighborhood of Markov random fields

Imre Csiszár and Zsolt Talata

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Abstract

For Markov random fields on ℤd with finite state space, we address the statistical estimation of the basic neighborhood, the smallest region that determines the conditional distribution at a site on the condition that the values at all other sites are given. A modification of the Bayesian Information Criterion, replacing likelihood by pseudo-likelihood, is proved to provide strongly consistent estimation from observing a realization of the field on increasing finite regions: the estimated basic neighborhood equals the true one eventually almost surely, not assuming any prior bound on the size of the latter. Stationarity of the Markov field is not required, and phase transition does not affect the results.

Article information

Source
Ann. Statist., Volume 34, Number 1 (2006), 123-145.

Dates
First available in Project Euclid: 2 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1146576258

Digital Object Identifier
doi:10.1214/009053605000000912

Mathematical Reviews number (MathSciNet)
MR2275237

Zentralblatt MATH identifier
1102.62105

Subjects
Primary: 60G60: Random fields62F12: Asymptotic properties of estimators
Secondary: 62M40: Random fields; image analysis82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Zsolt talata ku

Keywords
Markov random fieldpseudo-likelihoodGibbs measuremodel selectioninformation criteriontypicality

Zsolt Talata

Citation

Csiszár, Imre; Talata, Zsolt. Consistent estimation of the basic neighborhood of Markov random fields. Ann. Statist. 34 (2006), no. 1, 123--145. doi:10.1214/009053605000000912. https://projecteuclid.org/euclid.aos/1146576258


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Zsolt Talata works in mathematical statistics, overlapping with information theory and probability theory. He has worked on model selection problems using information criteria. His current research interest includes estimation of stationary ergodic processes in d-bar distance, context tree estimation of stationary ergodic processes, neighborhood estimation of Markov random fields, and longest increasing subsequence problems.

Teaching Interests

  • Mathematics
  • Statistics
  • Probability
  • Differential equations

Zsolt Talata Ng

Research Interests

  • Mathematical statistics
  • Information theory
  • Probability