1 / 7

Overview of Markov chains

Overview of Markov chains. David Gleich Purdue University Network & Matrix Computations Computer Science 15 Sept 2011. Lots of words. transient recurrent primitive regular ergodic periodic irreducible P erron root. P erron vector stationary distribution

kamala
Download Presentation

Overview of Markov chains

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Overview of Markov chains David Gleich Purdue University Network & Matrix Computations Computer Science 15 Sept 2011

  2. Lots of words transient recurrent primitive regular ergodic periodic irreducible Perron root Perron vector stationary distribution first transition analysis Cesáro limit reversible Markov chain simple stationary distribution Perron-Frobenius theorem

  3. Some theory • Theorem Let A ≥ 0 be irreducible then A has a unique positive eigenvector with eigenvalue equal to the spectral radius of A.

  4. In German Oskar Perron, MathematischeAnnalen, 64:248-263, 1907 doi: 10.1007/BF01449896

  5. Just kidding

  6. Important application • PageRank • centrality measures • spectral graph theory • random sampling

  7. Probable outline • Stochastic processes, Markov chains, and random walks, and stochastic matrices • The Perron-Frobenius theorem and stationary distribution • Hitting times, commute times, and other transition related problems

More Related