%0 Journal Article %1 HsuKoLePeSzeWo19 %A Hsu, D. %A Kontorovich, A. %A Levin, D. A. %A Peres, Y. %A Szepesvári, Cs. %A Wolfer, G. %D 2019 %J Annals of Applied Probability %K Markov a bounds, chains, data-dependent finite-sample mixing, posteriori theory %N 4 %P 2439--2480 %T Mixing Time Estimation in Reversible Markov Chains from a Single Sample Path %V 29 %X The spectral gap of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix P may be unknown, yet one sample of the chain up to a fixed time n may be observed. We consider here the problem of estimating the spectral gap from this data and give a fully empirical interval estimate, whose width is essentially unimprovable (shortened abstract).

@article{HsuKoLePeSzeWo19, abstract = {The spectral gap of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix P may be unknown, yet one sample of the chain up to a fixed time n may be observed. We consider here the problem of estimating the spectral gap from this data and give a fully empirical interval estimate, whose width is essentially unimprovable (shortened abstract).}, added-at = {2020-03-17T03:03:01.000+0100}, author = {Hsu, D. and Kontorovich, A. and Levin, D. A. and Peres, Y. and {Sz}epesv{\'a}ri, {Cs}. and Wolfer, G.}, biburl = {https://www.bibsonomy.org/bibtex/24433feed9c7777dc7f0b2bc73e2ff950/csaba}, date-added = {2019-07-24 20:08:32 -0600}, date-modified = {2019-07-24 20:17:30 -0600}, interhash = {66eeb3de0753e6463b4497b8b4f4bcfd}, intrahash = {4433feed9c7777dc7f0b2bc73e2ff950}, journal = {Annals of Applied Probability}, keywords = {Markov a bounds, chains, data-dependent finite-sample mixing, posteriori theory}, month = {July}, number = 4, pages = {2439--2480}, pdf = {papers/AAP19_mixing.pdf}, timestamp = {2020-03-17T03:03:01.000+0100}, title = {Mixing Time Estimation in Reversible {M}arkov Chains from a Single Sample Path}, volume = 29, year = 2019 }