JFIF, Photoshop 3.08BIM Z%G e USA i Web, news P David McKinney U Photographer s KU University Relations x ? G i% 'Zsolt Talata, Assistant Professor, Department. 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.

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

Zsolt Talata is a professor in the Mathematics department at University of Kansas - see what their students are saying about them or leave a rating yourself. Hee Sun Kim's 6 research works with 16 citations and 128 reads, including: (Engaging or avoiding) Change through Reflexive Practices. Zsolt Talata's research area is mathematical statistics, overlapping with information theory and probability theory. His research has been supported by the Division of Mathematical Sciences of the U.S. National Science Foundation and the Mathematical Sciences Division of the U.S. Army Research Office.

Zsolt talata ni
  • Mathematics
  • Statistics
  • Probability
  • Differential equations

Research Interests

  • Mathematical statistics
  • Information theory
  • Probability
  • 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

Zsolt Talata Sa

Zentralblatt MATH identifier
1102.62105

Zsolt Talata Na

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

Keywords
Markov random fieldpseudo-likelihoodGibbs measuremodel selectioninformation criteriontypicality

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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References

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