PPT-Classical (and Useful) Markov Chains

Markov Chains Seminar 9112016 Tomer Haimovich Outline Gamblers Ruin Coupon Collecting Hypercubes and the Ehrenfest Urn Model Random Walks on Groups Random Walks on   Gamblers Ruin. 1 Introduction Most of our study of probability has dealt with independent trials processes These processes are the basis of classical probability theory and much of statistics We have discussed two of the principal theorems The fundamental condition required is that for each pair of states ij the longrun rate at which the chain makes a transition from state to state equals the longrun rate at which the chain makes a transition from state to state ij ji 11 Twosided stat We will also see that we can 64257nd by merely solving a set of linear equations 11 Communication classes and irreducibility for Markov chains For a Markov chain with state space consider a pair of states ij We say that is reachable from denoted Nimantha . Thushan. Baranasuriya. Girisha. . Durrel. De Silva. Rahul . Singhal. Karthik. . Yadati. Ziling. . Zhou. Outline. Random Walks. Markov Chains. Applications. 2SAT. 3SAT. Card Shuffling. Part 4. The Story so far …. Def:. Markov Chain: collection of states together with a matrix of probabilities called transition matrix (. p. ij. ) where . p. ij. indicates the probability of switching from state S. Part 3. Sample Problems. Do problems 2, 3, 7, 8, 11 of the posted notes on . Markov Chains. Pizza Delivery Example. Pizza Delivery . Example. Will we get Pizza?. Start with s = <1, 0, 0, 0, 0, 0>. Find s = s P n-times.. A Preliminary . Investigation. By Andres Calderon Jaramillo. Mentor - Larry Lucas, Ph.D.. University of Central Oklahoma. Presentation Outline. Project description and literature review.. Musical background.. Markov Models. A. AAA. : 10%. A. AAC. : 15%. A. AAG. : 40%. A. AAT. : 35%. AAA. AAC. AAG. AAT. ACA. . . .. TTG. TTT. Training. Set. Building the model. How to find foreign genes?. Markov Models. . (part 2). 1. Haim Kaplan and Uri Zwick. Algorithms in Action. Tel Aviv University. Last updated: April . 18. . 2016. Reversible Markov chain. 2. A . distribution . is reversible . for a Markov chain if. (part 1). 1. Haim Kaplan and Uri Zwick. Algorithms in Action. Tel Aviv University. Last updated: April . 15 . 2016. (Finite, Discrete time) Markov chain. 2. A sequence . of random variables.  . Each . Quantum Hamiltonian Complexity. Aram Harrow (MIT). Simons Institute. 16 Jan 2014. Entanglement. Original motivation for quantum computing. [Feynman ‘82]. Nature isn't classical, dammit, and if you want to make a simulation of Nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.. regular Or Ergodic?. Absorbing state: A state in a . Markov . chain . that . you . cannot . leave, . i.e. . p. ii. = 1. . Absorbing . Markov chain. : . if it has at least one absorbing state and it is possible to reach that absorbing state from any other state. . . CS6800. Markov Chain :. a process with a finite number of states (or outcomes, or events) in which the probability of being in a particular state at step n + 1 depends only on the state occupied at step n.. 1. Probability and Time: Markov Models. Computer Science cpsc322, Lecture 31. (Textbook . Chpt. . 6.5.1). Nov, 22, 2013. CPSC 322, Lecture 30. Slide . 2. Lecture Overview. Recap . Temporal Probabilistic Models.