Luke Tierney. Markov chains for exploring posterior distributions. The Annals of Statistics, 22:17011762, 1994. Home/Search Document Not in Database Summary Related Articles Check |
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....de 1 : deM dh 1 : dhM da 1 : daN : To actually compute these conditional means is non trivial. To accomplish this, we used a Metropolis Algorithm. The Metropolis algorithm is an example of a Markov chain Monte Carlo Algorithm; for background see, e.g. Smith and Roberts [23] Tierney [24]; Gilks et al. 11] Roberts and Rosenthal [21] The Metropolis Algorithm proceeds by starting all the 2M N parameter values at 1. It then attempts, for each parameter in turn, to add an independent N(0; random variable to the parameter. It then accepts this new value with probability ....
L. Tierney. Markov chains for exploring posterior distributions (with discussion). Annals of Statistics, 22:1701-- 1762, 1994. 24 A Experiments A.1 Query: abortion (Base Set size = 2293)
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....1 . de n dh 1 . dh n da 1 . da n . To actually compute these conditional means is non trivial. To accomplish this, we used a Metropolis Algorithm. The Metropolis algorithm is an example of a Markov chain Monte Carlo Algorithm (for background see, e.g. Smith and Roberts [48] Tierney [49]; Gilks et al. 22] Roberts and Rosenthal [45] We denote this algorithm as BAYESIAN. The Metropolis Algorithm proceeds by starting all the 3n parameter values at 1. It then attempts, for each parameter in turn, to add an independent N(0, # ) random variable to the parameter. It then ....
L. Tierney. Markov chains for exploring posterior distributions (with discussion). Annals of Statistics, 22:1701--1762, 1994.
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....where we write P : Q d Q d 1 Q 1 , where Q k is the Markov kernel that replaces the k th coordinate by a draw from (dx k jfx j g j 6=k ) leaving x j xed for j 6= k. The random scan Gibbs sampler, P : d 1 P d i=1 Q i is sometimes used instead (see Smith and Roberts [22] Tierney [23]) When the full conditional distributions (dx i jfx j g j 6=i ) are dicult to sample, one can instead de ne new operators P i (e.g. one dimensional Metropolis algorithms) which are easily implemented, such that P i converges to Q i (in an appropriate sense) as n goes to in nity. This method is ....
....operators P i (e.g. one dimensional Metropolis algorithms) which are easily implemented, such that P i converges to Q i (in an appropriate sense) as n goes to in nity. This method is referred to as variable at a time Metropolis Hastings or Metropolis within Gibbs in the terminology of Tierney [23] and Chan and Geyer [1] Let C : P 1 ; P 2 ; P d ) be any collection of Markov kernels on a state space X = X 1 X d . The random scan hybrid sampler for C is the sampler P RS de ned by P RS : d (P 1 P d ) In this paper, we focus on the Random Scan Metropolis (RSM) ....
L. Tierney. Markov chains for exploring posterior distributions. Ann. Statist., 22(4):1701-1762, 1994. With discussion and a rejoinder by the author.
Convergence of Pseudo-Finite Markov Chains - Rosenthal (1992) (Correct)
....[BD] See [D] for background, examples, and references. For random walks on compact Lie groups, there has been some recent progress; see [R1] For more general Markov chains, the notion of Harris recurrence (see [A] AN] N] has proven useful in obtaining rates of convergence (see e.g. [T], R2] R3] Finite state space Markov chains remain the simplest case to study, because their convergence can be analyzed directly in terms of the finite spectrum of their transition kernel; see e.g. DS] In this paper, we identify a class of Markov chains, which we call pseudo finite , ....
L. Tierney (1991), Markov Chains for Exploring Posterior Distributions, Tech. Rep. 560, School of Statistics, University of Minnesota.
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....might run at di erent speeds; they might have di erent user loads on them; one or more of them might be down; etc. Handling these issues correctly is crucial to the success of parallel Monte Carlo. In addition, Markov chain Monte Carlo algorithms are now very common (see for example [17] 51] [53], 22] 45] and parallelising them presents additional diculties such as determining appropriate burn in time. We note that similar issues have been considered in various contexts in the operations research literature. In particular, in an excellent series of papers ( 23] 24] 25] 26] ....
....to depend on the speed at which the simulation happens to run, then it follows that a second run would not produce identical results even if started with the same pseudo random number seed. 4. Parallel Markov chain Monte Carlo. Markov chain Monte Carlo (MCMC) algorithms (see e.g. 17] 51] [53], 22] 45] such as the Gibbs sampler and the Metropolis Hastings algorithm, have become extremely popular in statistics (especially Bayesian statistics) as a method of approximately computing dicult high dimensional integrals. They are also used in theoretical computer science for approximate ....
L. Tierney (1994), Markov chains for exploring posterior distributions (with discussion). Ann. Stat. 22, 1701-1762.
Supervised Classification Using MCMC Methods - Davy, Doncarli, Tourneret (2000) (Correct)
....the convergence speed in many practical cases (see [1] or [6] More precisely, a random permutation is uniformly drawn. Each component is then updated according to this permutation and the acceptance probability (7) Each kernel is used in turn and the resulting hybrid stategy is called a cycle [10]. The resulting cycle kernel is clearly irreducible and aperiodic. Consequently, it is well known ( 2] p. l ) that the MC invariant distribution is also the limiting distribution. Moreover, the following ergodic theorem holds ( 2] p. l ) o T U X Y U 9 [ o T [ qp r s UktBuwvyx ....
L. Tierney, "Markov chains for exploring posterior distributions, " Annals of Stats., vol. 22, no 4, pp. 1701-1728, 1994.
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Luke Tierney. Markov chains for exploring posterior distributions. The Annals of Statistics, 22:17011762, 1994.
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Tierney L. (1994), Markov chains for exploring posterior distributions (with discussion). Ann. Stat. 22, 1701-1762.
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