2 edition of Rates of convergence for everywhere-positive markov chains found in the catalog.
Rates of convergence for everywhere-positive markov chains
John Robert Baxter
|Statement||J.R. Baxter and Jeffrey S. Rosenthal.|
|Series||Technical report series / University of Toronto, Dept. of Statistics -- 9406, Feb., (1994), Technical report (University of Toronto. Dept. of Statistics) -- no. 9406|
|Contributions||Rosenthal, Jeffrey S.|
|LC Classifications||QA274.7 .B38 1994|
|The Physical Object|
|Pagination||7 p. --|
I am currently working on rates of convergence of Markov chains with prof Vats and am learning about recent advances in probabilistic machine learning as part of Prof. Piyush Rai’s reading group. Additionally, I have enjoyed theoretical math courses on analysis and have had fun . A Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC).
Chapter 2 (September 10 ) General Markov Chains Chapter 3 (September 10 ) Reversible Markov Chains Chapter 4 (October 11 ) Hitting and Convergence Time, and Flow Rate, Parameters for Reversible Markov Chains Chapter (now Chapter 12) (October 11 ) untitled: does coupling theory and examples. ACM Markov Chains, Discrete Stochastic Processes and Applications. Last Update: Decem Homework: Sent via email to registered students (drop the instructor an email if you are not registered yet to be added to the email list). Lecture Notes: Sent via email to registered students Prerequisite: ACM/EE or CMS/ACM/EE or instructor agreement Piazza: for all class-related.
to Markov chains and using some facts from the number theory he showed when ergodicity holds. The classical theorem of Perron and Frobenius (which can be found for example in Seneta ) can be used to show that for ﬁnite state spaces, geometric rate of convergence holds (see e.g. Cinlar ). Front. Math. China (), – SPEED OF STABILITY FOR BIRTH–DEATH PROCESSES Mu-Fa Chen (Beijing Normal University) —Novem
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ELSEVIER Statistics & Probability Letters 22 () STATISTICS & PROBABILITY LETTERS Rates of convergence for everywhere-positive Markov chains J.R. Baxtera, Jeffrey S. Rosenthalb'* a School of Mathematics, University of Minnesota, Minneapolis, MNUSA b Department of Statistics, University of Toronto, Toronto, Ontario, Canada M5S 1A1 Cited by: RATES OF CONVERGENCE FOR EVERYWHERE-POSITIVE MARKOV CHAINS J.R.
Baxter* and Jeﬀrey S. Rosenthal** (January, ; revised March, ) 0. Introduction It is often useful to know that the distribution of a Markov process converges to a stationary distribution, and if possible to know how rapidly convergence takes place.
Such. T1 - Rates of convergence for everywhere-positive Markov chains. AU - Baxter, J. AU - Rosenthal, Jeffrey S. PY - /3. Y1 - /3. N2 - We generalize and simplify a result of Schervish and Carlin () concerning the convergence of Markov chains to their stationary by: In Theorem of the book Markov Chains and Mixing Times by Levin & Peres, A Markov chain that has this convergence rate is called geometric uniform ergodic.
Is this the fastest rate at which a Markov chain can converge. If true, is there a way to prove it. If false, are there examples of chains that converge at a rate faster than geometric.
Book Review: An introduction to probability theory and its applications Rates of convergence for everywhere-positive Markov chains. Article. () concerning the convergence of Markov.
Coupling Constructions and Convergence of Markov Chains 10 Couplings for the Ehrenfest Urn and Random-to-Top Shufﬂing 12 The Coupon Collector’s Problem 13 Exercises 15 Convergence Rates for the Ehrenfest Urn and Random-to-Top 16 Exercises 17 3.
Spectral Analysis 18 Transition Kernel of a Reversible Markov. This paper studies aspects of the Siegmund dual of the Markov branching process. The principal results are optimal convergence rates of its transition function and limit theorems in the case that it is Rates of convergence for everywhere-positive markov chains book positive recurrent.
Additional discussion is given about specifications of the Markov branching process and its dual. The dualising Markov branching processes need not be regular or even. (A later version of this paper, called \Convergence rates of Markov chains", was published in SIAM Review, ) Summary. This is an expository paper which presents certain basic ideas related to non-asymptotic rates of convergence for Markov chains.
In particular, we describe eigenvalue. This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments.
The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods.
The book is self-contained while all the results are carefully and concisely proven. For finite Markov chains the eigenvalues of P can be used to characterize the chain and also determine the geometric rate at which P n converges to Q in case P is ergodic.
For infinite Markov chains the spectrum of P plays the analogous role. It follows from Theorem that ‖P n −Q‖⩽Cβ n if and only if P is strongly ergodic. The best possible rate for β is the spectral radius of P.
I was studying rates of convergence of finite state space Markov chains. He made it clear that, for him, finite state space Markov chains is a trivial subject. Hurt but undaunted, I explained some of our results and methods.
He thought about it and said, “I see, yes, those are very hard problems”. Recently, the authors (see [1–4]) gave the bounds of convergence rates for Markov chains.
Their main methods are based on renewal theory and coupling theory. And in [5–7], the authors gave the convergence rates of stochastically monotone Markov chains. Their results and methods have the advantages of being applicable to some Markov chains.
Convergence properties of continuous-time Markov chains with application to target search. Proceedings of theAmerican Control Conference,Stochastic Strategies for Autonomous Robotic Surveillance. Finite inhomogeneous continuous-time Markov chains are studied. For a wide class of such processes an approach is proposed for obtaining sharp bounds on the rate of convergence to the limiting characteristics.
Queueing examples are considered. Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds.
Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments. This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space.
The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Hidden Markov Model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process – call it – with unobservable ("hidden") assumes that there is another process whose behavior "depends" goal is to learn about by stipulates that, for each time instance, the conditional probability distribution of given the history.
Nash Inequalities for Finite Markov Chains P. Diaconis I and L. Saloff-Coste 2 Received November 4, ; revised August 6, This paper develops bounds on the rate of decay of powers of Markov kernels on finite state spaces.
These are combined with eigenvalue estimates to give. 6 CONTENTS B Mathematical tools B.1 Elementary conditional probabilities B.2 Some formulaes for sums and series B.3 Some results for matrices B.4 First order differential equations B.5 Second order linear recurrence equations B.6 The ratio test B.7 Integral test for convergence B.8 How to do certain computations in R C Proofs of selected results Artificial immune algorithm has been used widely and successfully in many computational optimization areas, but the theoretical research exploring the convergence rate characteristics of artificial immune algorithm is yet inadequate.
In this paper, i. The modern theory of Markov chain mixing is the result of the convergence, in the ’s and ’s, of several threads. (We mention only a few names here; see the chapter Notes for references.) For statistical physicists Markov chains become useful in Monte Carlo simu-lation, especially for models on nite grids.
The mixing time can.Then, the results are applied to study theL 2-convergence for Markov chains and for a diffusion on compact manifold. The estimate of the convergent rate provided by this method can be sharp. View.In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the more steps that are included, the more closely the distribution of the.