Extremal indices, geometric ergodicity of Markov chains, and MCMC

Roberts, Gareth O.;Rosenthal, Jeffrey S.;Segers, Johan;Sousa, Bruno
(2006) , 17 pages

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Authors
  • Roberts, Gareth O.Universidade do Minho
    Author
  • Rosenthal, Jeffrey S.Universidade do Minho
    Author
  • Segers, JohanUCLouvain
    Author
  • Sousa, BrunoUniversidade do Minho
    Author
Abstract
We investigate the connections between extremal indices on the one hand and stability of Markov chains on the other hand. Both theories relate to the tail behaviour of stochastic processes, and we find a close link between the extremal index and geometric ergodicity. Our results are illustrated throughout with examples from simple MCMC chains.
Affiliations
  • Institution iconUCLouvainEUEN/STAT - Institut de statistique
  • Lancaster universityDepartment of Mathematics and Statistics
  • University of TorontoDepartment of Statistics
  • Universidade do MinhoDepartamento de Matemática para a Ciência e Tecnologia

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Roberts, G. O., Rosenthal, J. S., Segers, J., & Sousa, B. (2006). Extremal indices, geometric ergodicity of Markov chains, and MCMC (Stat Discussion Paper 0622). https://hdl.handle.net/2078.5/65364