Elements of S can be interpreted as various possible states of whatever system we are interested in studying, and pij represents the probability that the system is in state j at time n+ 1, if it is state i at time n. We will think of a Markov chain as a stochastic process with ...
The main component in the running time of the MCMC algorithm is the “mixing time” of the underlying Markov chain., i.e., the number of steps one needs to run the chain to approximate the stationary distribution well. Welcome to the webpage of this course on Markov chains and mixing t...
A Markov chain (discrete-time Markov chain or DTMC[1]), named after Andrey Markov, is a random process that undergoes transitions from one state to another on a state space. It must possess a property that is usually characterized as "memoryless": the probability distribution of the next ...
We model the dispatching process in rideshare as a Markov chain that takes into account the geographic mobility of both drivers and riders over time. Prior work explores dispatch policies in the limit of such Markov chains; we characterize when this limit assumption is valid, under a variety of...
Markov chain Minorization Mixing time Randomized algorithm Stopping timeConsider the class of discrete time, general state space Markov chains which satisfy a "uniform ergodicity under sampling" condition. There are many ways to quantify the notion of "mixing time", i.e., time to approach ...
Compute the stationary distribution of a Markov chain, estimate its mixing time, and determine whether the chain is ergodic and reducible. Compare Markov Chain Mixing Times Compare the estimated mixing times of several Markov chains with different structures. ...
Def. The mixing time of a Markov chain istmix(ε)=min{t:d(t)≤ε}.tmix=tmix(14),tmix(ε)≤ln1εtmix.tave(ε)=min{t:max‖at−π‖1≤ε}.remark: tave exists without the assumption that MC is aperiodic. For aperiodic chains, tmix(ε)<tave(ε)...
Since the publication of the first edition, the field of mixing times has continued to enjoy rapid expansion. In particular, many of the open problems posed in the first edition have been solved. The book has been used in courses at numerous universities, motivating us to update it. In the...
Geometric bounds on the fastest mixing Markov chain Article Open access 30 January 2024 Mixing times and hitting times for general Markov processes Article Open access 09 October 2023 Maximum Kolmogorov-Sinai Entropy Versus Minimum Mixing Time in Markov Chains Article 21 November 2017 References...
Markov Chain Monte CarloSNRinteger least-square optimization problemsinteger least-square problemslattice structureIn this paper, we study the mixing time of Markov Chain Monte Carlo (MCMC) for integer least-square (LS) optimization problems. It is found that the mixing time of MCMC for integer ...