Kranthi K. Gade's research while affiliated with CUNY Graduate Center and other places

Publication (1)

Article
We consider the problem of optimizing the asymptotic convergence rate of a parameter-dependent nonreversible Markov chain. We begin with a single-parameter case studied by Diaconis, Holmes and Neal and then introduce multiple parameters. We use nonsmooth analysis to investigate whether the presence of multiple parameters allows a faster asymptotic...

Citations

... Subsection 3.1) with the pµ, Qq´reversible transition P 1 α " p1´αqId`αQ for α P r0, 1s, as suggested in [16] (see also references therein). The analysis of [16] (see also [24]), in the situation where π is the uniform distribution, shows that near optimal convergence speed to equilibrium is achieved for αpdq " c{d ą 0, whereas application of Theorem 3.4 shows that α closer to zero is a better choice when asymptotic variance is of interest, since Epg, QP 1 α q " p1´αq{2 ş rgpx, vq´gpx,´vqs 2 µ`dpx, vq˘. To the best of our knowledge no systematic spectral theory exists in the setup considered in this manuscript, despite the numerous analogies with the µ´selfadjoint scenario and its practical interest. ...