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This article provides the first procedure for computing a fullydata-dependent interval that traps the mixing time $t_{\text{mix}}$ of a finitereversible ergodic Markov chain at a prescribed confidence level. The intervalis computed from a single finite-length sample path from the Markov chain, anddoes not require the knowledge of any parameters of the chain. This stands incontrast to previous approaches, which either only provide point estimates, orrequire a reset mechanism, or additional prior knowledge. The interval isconstructed around the relaxation time $t_{\text{relax}}$, which is stronglyrelated to the mixing time, and the width of the interval converges to zeroroughly at a $\sqrt{n}$ rate, where $n$ is the length of the sample path. Upperand lower bounds are given on the number of samples required to achieveconstant-factor multiplicative accuracy. The lower bounds indicate that, unlessfurther restrictions are placed on the chain, no procedure can achieve thisaccuracy level before seeing each state at least $\Omega(t_{\text{relax}})$times on the average. Finally, future directions of research are identified.

Mixing Time Estimation in Reversible Markov Chains from a Single Sample Path