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Naive asymptotics for hitting time bounds in Markov chains

1992
*
Acta Informatica
*

While obtaining expected passage limes is smelly a numerical procedure

doi:10.1007/bf01185562
fatcat:vhmfcf34q5c5fevzgie5qmump4
*for*general*Markov**chains*, the results presented here outline a simple approach to*bound*expected passage*times*provided the*chains*... A set of sufficient conilitions is obtained*for**Markov**chains*to yield upper and lower passage lime*bounds*. ... Uppuluri RelO of ORNL*for*their mosl helpfUl comments. ...##
###
Page 4470 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
*
Mathematical Reviews
*

Dean Isaacson (1-IASU-S)
60 PROBABILITY THEORY AND STOCHASTIC PROCESSES
93h:60109 60510 68Q25
Rego, Vernon (1-PURD-C)

*Naive**asymptotics**for**hitting**time**bounds**in**Markov**chains*. ... Summary: “A set of sufficient conditions is obtained*for**Markov**chains*to yield upper and lower passage*time**bounds*. ...##
###
Markov Chain Monte Carlo Algorithms: Theory and Practice
[chapter]

2009
*
Monte Carlo and Quasi-Monte Carlo Methods 2008
*

We describe the importance and widespread use of

doi:10.1007/978-3-642-04107-5_9
fatcat:royg2nehd5gvfnqhqryl6ig4a4
*Markov**chain*Monte Carlo (MCMC) algorithms, with an emphasis on the ways*in*which theoretical analysis can help with their practical implementation. ...*In*particular, we discuss how to achieve rigorous quantitative*bounds*on convergence to stationarity using the coupling method together with drift and minorisation conditions. ... At last count, the MCMC Preprint Service lists about seven thousand research papers, and the phrase "*Markov**chain*Monte Carlo" elicits over three hundred thousand*hits**in*Google. ...##
###
Importance sampling for Markov chains

1996
*
Proceedings of the 28th conference on Winter simulation - WSC '96
*

*In*this paper we describe several computational algorithms useful

*in*studying importance sampling (IS)

*for*

*Markov*

*chains*. ... We consider two classes of problems:

*hitting*

*times*and fixed-horizon costs. ... L: (x) = Ep [g (x)] M TF = E p ['L1i] = Ep [1i]Ep [M]. i=l

*HITTING*

*TIMES*Consider a continuous-

*time*

*Markov*

*chain*defined on a finite state space 5. ...

##
###
Structured variational methods for distributed inference: Convergence analysis and performance-complexity tradeoff

2009
*
2009 IEEE International Symposium on Information Theory
*

performance

doi:10.1109/isit.2009.5205928
dblp:conf/isit/ZhangD09
fatcat:ua63ooshjvd7pbgimz7ad4ddi4
*in*given*time*). ... correspond to edge processes, typically involving non-reversible*Markov**chains*. ... Then by the Chernoff*bound*, the probability that there is at least one*time*that the walk*hits*the boundary edges before expected*time*to*hit*a boundary node*in*a cluster and the coupling*time**in*the ...##
###
Page 7234 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
*
Mathematical Reviews
*

*time*of a specific state

*in*the case of a finite state ergodic

*Markov*

*chain*. ... Summary: “The Bayesian bootstrap

*for*

*Markov*

*chains*is the Bayesian analogue of the bootstrap method

*for*

*Markov*

*chains*. ...

##
###
Testing Symmetric Markov Chains from a Single Trajectory
[article]

2017
*
arXiv
*
pre-print

the

arXiv:1704.06850v2
fatcat:ka6snzgo4rf43nofn6ebik2wda
*hitting**times*of the model*chain*M0 is O(n)*in*the size of the state space n. ... We provide efficient testers and information-theoretic lower*bounds**for*testing identity of symmetric*Markov**chains*under our proposed measure of difference, which are tight up to logarithmic factors if ...*Hitting**Times*and Mixing*Times*Two commonly studied random variables associated with*Markov**chains*which are relevant to this paper are their mixing*times*and*hitting**times*. ...##
###
Discrete Hit-and-Run for Sampling Points from Arbitrary Distributions Over Subsets of Integer Hyperrectangles

2009
*
Operations Research
*

To surmount this difficulty, we propose Discrete

doi:10.1287/opre.1080.0600
fatcat:6ape5mvpube4na2yr7li2lohlm
*Hit*-and-Run (DHR), a*Markov**chain*motivated by the*Hit*-and-Run algorithm known to be the most efficient method*for*sampling from log-concave distributions ...*In*addition to this*asymptotic*analysis, we investigate finite-*time*behavior of DHR and present a variety of examples where DHR exhibits polynomial performance. ... by a membership oracle, and hence can be employed*for*approximate sampling from π over S, and (ii) compute finite-*time*performance*bounds**for*this*Markov**chain*sampler*for*some special cases of S and π ...##
###
Bootstrap uniform central limit theorems for Harris recurrent Markov chains
[article]

2016
*
arXiv
*
pre-print

The main objective of this paper is to establish bootstrap uniform functional central limit theorem

arXiv:1601.01470v1
fatcat:atqi6p7cevdlfmbhq2njlhkoa4
*for*Harris recurrent*Markov**chains*over uniformly*bounded*classes of functions. ... We show that*in*the atomic case the proof of the bootstrap uniform central limit theorem*for**Markov**chains**for*functions dominated by a function*in*L^2 space proposed by Radulović (2004) can be significantly ... Let τ A = τ A (1) = inf{n ≥ 1 : X n ∈ A} be the first*time*when the*chain**hits*the regeneration set A and τ A (j) = inf{n > τ A (j − 1), X n ∈ A}*for*j ≥ 2. ...##
###
Markov Kernels Local Aggregation for Noise Vanishing Distribution Sampling
[article]

2022
*
arXiv
*
pre-print

Some examples

arXiv:1806.09000v2
fatcat:jq5qxmfl2zfzvgdvlh47id3xqu
*for*which we show (theoretically or empirically) that a locally-weighted aggregation converges substantially faster and yields smaller*asymptotic*variances than an equivalent random-scan ... to a kernel which is relevant*for*the local topology of the target distribution. ... Explicit*bounds*on related*asymptotic*quantities such as the rate of convergence of the*Markov**chain*(*for*example*in*total variation) or its*asymptotic*variance (*for*squared integrable functions) may be ...##
###
On The Memory Complexity of Uniformity Testing
[article]

2022
*
arXiv
*
pre-print

Prior works

arXiv:2206.09395v1
fatcat:oc6rklbn4rfsbhfox2gerai3em
*in*the field have almost exclusively used collision counting*for*upper*bounds*, and the Paninski mixture*for*lower*bounds*. ... Thus, different proof techniques are needed*in*order to attain our*bounds*. ... erg ) be the*asymptotic*probability of success*in*the new ergodic*chain*. ...##
###
Multi-scale metastable dynamics and the asymptotic stationary distribution of perturbed Markov chains
[article]

2014
*
arXiv
*
pre-print

We consider a simple but important class of metastable discrete

arXiv:1412.6979v1
fatcat:winkuxckgzdkhh4to6amahgmve
*time**Markov**chains*, which we call perturbed*Markov**chains*. ... Closed probabilistic expressions are given*for*the*asymptotic*transition probabilities of these*chains*, but we also show how to compute them*in*a fast and numerically stable way. ...*For*a*Markov**chain*X on a state space S, the*hitting**time*of a set A ⊂ S is denoted by τ A (X) = inf{n 0 : X n ∈ A}, and the return*time*by τ + A (X) = inf{n > 0 : X n ∈ A}. ...##
###
Rates of convergence for lamplighter processes

1997
*
Stochastic Processes and their Applications
*

Consider a graph, G,

doi:10.1016/s0304-4149(97)00007-0
fatcat:y4ekchgjorer3kltcothc64ihm
*for*which the vertices can have two modes, 0 or 1. Suppose that a particle moves around on G according to a discrete*time**Markov**chain*with the following rules. ...*In*the latter case we show that the convergence rate is*asymptotically*determined by the cover*time*CN*in*that the total variation norm after aN2 steps is given by P(CN > UN'). ... Acknowledgements We thank the referee*for*valuable comments and corrections. 0. Hiiggstrijm, J. JonassonlStochastic Processes and their Applications 67 (1997) 227-249 ...##
###
Adaptive Importance Sampling Technique for Markov Chains Using Stochastic Approximation

2006
*
Operations Research
*

*For*a discrete-

*time*finite-state

*Markov*

*chain*, we develop an adaptive importance sampling scheme to estimate the expected total cost before

*hitting*a set of terminal states. ... The updates are shown to concentrate

*asymptotically*

*in*a neighborhood of the desired zero variance estimator. ... Acknowledgements: The authors would like to thank the area editor, the associate editor and the referees

*for*their inputs that led to considerable improvements

*in*the paper. ...

##
###
Stochastic Optimization on Continuous Domains With Finite-Time Guarantees by Markov Chain Monte Carlo Methods

2010
*
IEEE Transactions on Automatic Control
*

We introduce

doi:10.1109/tac.2010.2078170
fatcat:e4kxu2v2dbdzjbvmrdeso4d6f4
*bounds*on the finite-*time*performance of*Markov**chain*Monte Carlo algorithms*in*approaching the global solution of stochastic optimization problems over continuous domains. ... A comparison with other state-of-the-art methods having finite-*time*guarantees*for*solving stochastic programming problems is included. ... Weak convergence to 1 implies that,*asymptotically*, k*hits*the set of approximate value optimizers 2 3 (),*for*any > 0, with probability one [21] - [25] . ...
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