W.K. Yuen, Applications of geometric bounds to the convergence rate of Markov chains on R , Stochastic processes and their Applications 87 (2000) 1-23.  Home/Search Document Details and Download
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Honest Exploration of Intractable Probability Distributions.. - Jones, Hobert (2001) (Correct)
.... where X is nite (but very large) see e.g. Diaconis and Stroock 1991) Applications of such techniques in MCMC contexts include Frigessi, di Stefano, Hwang and Sheu (1993) and Ingrassia (1994) Unfortunately, these methods are not directly applicable to chains on general state spaces (but see Yuen 2000). We know that for any xed B 2 f0; 1; g, h n;B is a strongly consistent estimator of E h. We now seek a reliable measure of its accuracy. Suppose that the following CLT holds p n h n;B E h d N 0; 2 h : 12) Then given an estimate of 2 h , we could get an ....
Yuen, W. K. (2000). Applications of geometric bounds to the convergence rate of Markov chains on R n , Stochastic Processes and Their Applications 87: 1-23.
Application of Geometric Bounds to Convergence Rates of Markov.. - Yuen (2001) (1 citation) Self-citation (Yuen) (Correct)
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W.K. Yuen, Applications of geometric bounds to the convergence rate of Markov chains on R , Stochastic processes and their Applications 87 (2000) 1-23.
Generalization of Discrete-time Geometric Bounds to Convergence.. - Yuen (2001) Self-citation (Yuen) (Correct)
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W.K. Yuen, Applications of geometric bounds to the convergence rate of Markov chains on R , Stochastic processes and their Applications 87 (2000) 1-23. 38
Applications of Geometric Bounds to the Convergence Rate of Markov .. - Yuen (2000) (1 citation) Self-citation (Yuen) (Correct)
....di usions will be studied using the limit Cheeger s bound. An n dimensional di usion will be studied using the limit path bound. We conclude the thesis with Chapter 5 and discuss some possible development and improvement in the future. Parts of Chapters 1, 2 and 3 were already published in Yuen [44]. 1.2 Basic Notations and the Cheeger s Inequality In this section, we describe the type of Markov chains and Markov processes considered in this thesis. We rst give some informal de nitions on Markov chains and Markov processes we considered in this thesis. Let F be a countably generated ....
W.K. Yuen, Applications of geometric bounds to the convergence rate of Markov chains on R n , Stochastic processes and their Applications 87 (2000) 1-23.
Generalization of Discrete-time Geometric Bounds to Convergence.. - Yuen (2000) Self-citation (Yuen) (Correct)
....used a geometric argument with paths to bound the Cheeger s constant for a discrete time nite space Markov chain. Diaconis and Stroock (1991) and Sinclair (1992) used a similar geometric arguments with paths to bound the second largest eigenvalue of a self adjoint discrete time Markov chain. Yuen [39] generalized the path argument to bound the spectral gap of a discrete time Markov chain on R n : In this paper, by considering some form of limits, we generalize some discrete time results to bound the convergence rate of a reversible continuous time Markov process. We shall derive some ....
....reversible Markov 8 chain (discrete or continuous time) on R n described in 1.2. In both cases, we obtain upper bounds for 1 (P ) de ned in (5) These bounds are called path bounds as each bound is associated with a set of paths. The proofs of the results in this section can be found in Yuen [39]. We assume that the transition kernel is of the form P (x; dy) x) x (dy) p x (y)dy where x is the unit point mass on x for any x 2 R n . Suppose the invariant distribution has density q(y) w.r.t. Lebesgue measure. The next requirement is the existence of a set of paths satisfying some ....
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W.K. Yuen, Applications of geometric bounds to the convergence rate of Markov chains on R n , Stochastic processes and their Applications 87 (2000) 1-23. 37
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