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33
Exchangeable pairs and Poisson approximation
 Probab. Surv
, 2005
"... This is a survery paper on Poisson approximation using Stein’s method of exchangeable pairs. We illustrate using Poissonbinomial trials and many variations on three classical problems of combinatorial probability: the matching problem, the coupon collector’s problem, and the birthday problem. While ..."
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Cited by 26 (7 self)
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This is a survery paper on Poisson approximation using Stein’s method of exchangeable pairs. We illustrate using Poissonbinomial trials and many variations on three classical problems of combinatorial probability: the matching problem, the coupon collector’s problem, and the birthday problem. While many details are new, the results are closely related to a body of work developed by Andrew Barbour, Louis Chen, Richard Arratia, Lou Gordon, Larry Goldstein, and their collaborators. Some comparison with these other approaches is offered. 1
On adding a list of numbers (and other onedependent determinantal processes
 Bull. Amer. Math. Soc
"... Abstract Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a onedependent determinantal point process. This makes it easy to answer natural questions: How many carri ..."
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Abstract Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a onedependent determinantal point process. This makes it easy to answer natural questions: How many carries are typical? Where are they located? We show that many further examples, from combinatorics, algebra and group theory, have essentially the same neat formulae, and that any onedependent point process on the integers is determinantal. The examples give a gentle introduction to the emerging fields of onedependent and determinantal point processes.
Stein’s Method and Nonreversible Markov Chains. Stein’s method: expository lectures and applications
 69–77, IMS Lecture
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Theorems and Conjectures Involving Rook Polynomials with Real Roots
 in Proc. Topics in Number Theory and Combinatorics, State
, 1997
"... Let A = (a ij ) be a real n \Theta n matrix with nonnegative entries which are weakly increasing down columns. If B = (b ij ) is the n \Theta n matrix where b ij := a ij +z; then we conjecture that all of the roots of the permanent of B, as a polynomial in z; are real. Here we establish several ..."
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Cited by 14 (4 self)
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Let A = (a ij ) be a real n \Theta n matrix with nonnegative entries which are weakly increasing down columns. If B = (b ij ) is the n \Theta n matrix where b ij := a ij +z; then we conjecture that all of the roots of the permanent of B, as a polynomial in z; are real. Here we establish several special cases of the conjecture.
CARRIES, SHUFFLING, AND SYMMETRIC FUNCTIONS
, 2009
"... The “carries” when n random numbers are added base b form a Markov chain with an “amazing” transition matrix determined by Holte [24]. This same Markov chain occurs in following the number of descents or rising sequences when n cards are repeatedly riffle shuffled. We give generating and symmetric f ..."
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Cited by 14 (6 self)
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The “carries” when n random numbers are added base b form a Markov chain with an “amazing” transition matrix determined by Holte [24]. This same Markov chain occurs in following the number of descents or rising sequences when n cards are repeatedly riffle shuffled. We give generating and symmetric function proofs and determine the rate of convergence of this Markov chain to stationarity. Similar results are given for type B shuffles. We also develop connections with Gaussian autoregressive processes and the Veronese mapping of commutative algebra.
Exploring the noisy threshold function in designing bayesian networks
 In Proceedings of SGAI International Conference on Innovative Techniques and Applications of Artificial Intelligence
, 2005
"... Causal independence modelling is a wellknown method both for reducing the size of probability tables and for explaining the underlying mechanisms in Bayesian networks. Many Bayesian network models incorporate causal independence assumptions; however, only the noisy OR and noisy AND, two examples of ..."
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Cited by 5 (1 self)
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Causal independence modelling is a wellknown method both for reducing the size of probability tables and for explaining the underlying mechanisms in Bayesian networks. Many Bayesian network models incorporate causal independence assumptions; however, only the noisy OR and noisy AND, two examples of causal independence models, are used in practice. Their underlying assumption that either at least one cause, or all causes together, give rise to an effect, however, seems unnecessarily restrictive. In the present paper a new, more flexible, causal independence model is proposed, based on the Boolean threshold function. A connection is established between conditional probability distributions based on the noisy threshold model and Poisson binomial distributions, and the basic properties of this probability distribution are studied in some depth. The successful application of the noisy threshold model in the refinement of a Bayesian network for the diagnosis and treatment of ventilatorassociated pneumonia demonstrates the practical value of the presented theory. 1
CENTRAL AND LOCAL LIMIT THEOREMS FOR EXCEDANCES BY CONJUGACY CLASS AND BY DERANGEMENT
"... We give central and local limit theorems for the number of excedances of a uniformly distributed random permutation belonging to certain sequences of conjugacy classes and belonging to the sequence of derangements. 1. ..."
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We give central and local limit theorems for the number of excedances of a uniformly distributed random permutation belonging to certain sequences of conjugacy classes and belonging to the sequence of derangements. 1.