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21
On the genealogy of large populations
, 1982
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Cited by 171 (0 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Geometric Ergodicity and Hybrid Markov Chains
, 1997
"... Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the socalled hybrid ..."
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Cited by 80 (25 self)
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Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the socalled hybrid chains. We prove that under certain conditions, a hybrid chain will "inherit" the geometric ergodicity of its constituent parts. 1 Introduction A question of increasing importance in the Markov chain Monte Carlo literature (Gelfand and Smith, 1990; Smith and Roberts, 1993) is the issue of geometric ergodicity of Markov chains (Tierney, 1994, Section 3.2; Meyn and Tweedie, 1993, Chapters 15 and 16; Roberts and Tweedie, 1996). However, there are a number of different notions of the phrase "geometrically ergodic", depending on perspective (total variation distance vs. in L 2 ; with reference to a particular V function; etc.). One goal of this paper is to review and clarify the relationship...
Coalescent Random Forests
 J. COMBINATORIAL THEORY A
, 1998
"... Various enumerations of labeled trees and forests, including Cayley's formula n n\Gamma2 for the number of trees labeled by [n], and Cayley's multinomial expansion over trees, are derived from the following coalescent construction of a sequence of random forests (R n ; R n\Gamma1 ; : ..."
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Cited by 39 (18 self)
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Various enumerations of labeled trees and forests, including Cayley's formula n n\Gamma2 for the number of trees labeled by [n], and Cayley's multinomial expansion over trees, are derived from the following coalescent construction of a sequence of random forests (R n ; R n\Gamma1 ; : : : ; R 1 ) such that R k has uniform distribution over the set of all forests of k rooted trees labeled by [n]. Let R n be the trivial forest with n root vertices and no edges. For n k 2, given that R n ; : : : ; R k have been defined so that R k is a rooted forest of k trees, define R k\Gamma1 by addition to R k of a single edge picked uniformly at random from the set of n(k \Gamma 1) edges which when added to R k yield a rooted forest of k \Gamma 1 trees. This coalescent construction is related to a model for a physical process of clustering or coagulation, the additive coalescent in which a system of masses is subject to binary coalescent collisions, with each pair of masses of magnitude...
Learning and Value Function Approximation in Complex Decision Processes
, 1998
"... In principle, a wide variety of sequential decision problems  ranging from dynamic resource allocation in telecommunication networks to financial risk management  can be formulated in terms of stochastic control and solved by the algorithms of dynamic programming. Such algorithms compute and sto ..."
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Cited by 38 (4 self)
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In principle, a wide variety of sequential decision problems  ranging from dynamic resource allocation in telecommunication networks to financial risk management  can be formulated in terms of stochastic control and solved by the algorithms of dynamic programming. Such algorithms compute and store a value function, which evaluates expected future reward as a function of current state. Unfortunately, exact computation of the value function typically requires time and storage that grow proportionately with the number of states, and consequently, the enormous state spaces that arise in practical applications render the algorithms intractable. In this thesis, we study tractable methods that approximate the value function. Our work builds on research in an area of artificial intelligence known as reinforcement learning. A point of focus of this thesis is temporaldifference learning  a stochastic algorithm inspired to some extent by phenomena observed in animal behavior. Given a selection of...
On the number of optimal base 2 representations of integers
 DESIGNS, CODES, CRYPTOGR
, 2006
"... We study representations of integers n in binary expansions using the digits 0, ±1. We analyze the average number of such representations of minimal “weight” ( = number of nonzero digits). The asymptotic main term of this average involves a periodically oscillating function, which is analyzed in ..."
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Cited by 7 (5 self)
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We study representations of integers n in binary expansions using the digits 0, ±1. We analyze the average number of such representations of minimal “weight” ( = number of nonzero digits). The asymptotic main term of this average involves a periodically oscillating function, which is analyzed in some detail. The main tool is the construction of a measure on [−1,1], which encodes the number of representations.
Generalised Stochastic Automaton Image Compression
, 1997
"... It is well known that digital images can be generated by generalised stochastic automata (GSA). This fact has been taken as the basis for image compression by storing a GSA rather than the image that it generates. This paper investigates fundamental relationships between the parameters of GSA and th ..."
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Cited by 3 (2 self)
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It is well known that digital images can be generated by generalised stochastic automata (GSA). This fact has been taken as the basis for image compression by storing a GSA rather than the image that it generates. This paper investigates fundamental relationships between the parameters of GSA and their generated images. In particular, we are interested in expressing the magnitude of GSA weights, and the precision to which they must be specified in image parameter terms. The significance of these relationships is connected to the compression ratio. An additional consequence of the use of GSA theory is a simplification and extension of current work in automaton based image compression.
A unified multiresolution coalescent: Markov lumpings of the KingmanTajima ncoalescent
, 2009
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Coalescent experiments I: Unlabeled ncoalescent and the site frequency spectrum
, 2009
"... We derive the transition structure of a Markovian lumping of Kingman’s ncoalescent [1, 2]. Lumping a Markov chain is meant in the sense of [3, def. 6.3.1]. The lumped Markov process, referred as the unlabeled ncoalescent, is a continuoustime Markov chain on the set of all integer partitions of ..."
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Cited by 2 (2 self)
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We derive the transition structure of a Markovian lumping of Kingman’s ncoalescent [1, 2]. Lumping a Markov chain is meant in the sense of [3, def. 6.3.1]. The lumped Markov process, referred as the unlabeled ncoalescent, is a continuoustime Markov chain on the set of all integer partitions of the sample size n. We derive the backwardtransition, forwardtransition, statespecific, and sequencespecific probabilities of this chain. We show that the likelihood of any given sitefrequencyspectrum (SFS), a commonly used statistics in genome scans, from a locus free of intralocus recombination, can be directly obtained by integrating conditional realizations of the unlabeled ncoalescent. We develop a controlled Markov chain for importance sampling such integrals from an augmented unlabeled ncoalescent forward in time. We apply the methods to populationgenetic data to conduct demographic inference at the empirical resolution of the sitefrequencyspectra. We also extend a family of classical hypothesis tests of standard neutrality