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99
Estimating a Dirichlet distribution
, 2000
"... The Dirichlet distribution and its compound variant, the Dirichletmultinomial, are two of the most basic models for proportional data, such as the mix of vocabulary words in a text document. Yet the maximumlikelihood estimate of these distributions is not available in closedform. This paper descr ..."
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Cited by 136 (1 self)
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The Dirichlet distribution and its compound variant, the Dirichletmultinomial, are two of the most basic models for proportional data, such as the mix of vocabulary words in a text document. Yet the maximumlikelihood estimate of these distributions is not available in closedform. This paper describes simple and efficient iterative schemes for obtaining parameter estimates in these models. In each case, a fixedpoint iteration and a NewtonRaphson (or generalized NewtonRaphson) iteration is provided. 1 The Dirichlet distribution The Dirichlet distribution is a model of how proportions vary. Let p denote a random vector whose elements sum to 1, so that pk represents the proportion of item k. Under the Dirichlet model with parameter vector α, the probability density at p is p(p) ∼ D(α1,...,αK) = Γ(∑k αk) k Γ(αk)
A point process framework for relating neural spiking activity to spiking history, neural ensemble and extrinsic covariate effects
 J. Neurophysiol
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Internet topology: connectivity of IP graphs
, 2001
"... In this paper we introduce a framework for analyzing local properties of Internet connectivity. We compare BGP and probed topology data, finding that currently probed topology data yields much denser coverage of ASlevel connectivity. We describe data acquisition and construction of several IPlevel ..."
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Cited by 86 (6 self)
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In this paper we introduce a framework for analyzing local properties of Internet connectivity. We compare BGP and probed topology data, finding that currently probed topology data yields much denser coverage of ASlevel connectivity. We describe data acquisition and construction of several IPlevel graphs derived from a collection of 220M skitter traceroutes. We find that a graph consisting of IP nodes and links contains 90.5% of its 629K nodes in the acyclic subgraph. In particular, 55% of the IP nodes are in trees. Full bidirectional connectivity is observed for a giant component containing 8.3% of IP nodes.
The TimeRescaling Theorem and Its Application to Neural Spike Train Data Analysis
 NEURAL COMPUTATION
, 2001
"... Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model’s validity prior to using it to make inferences about a particular neural system. Assessing goodnessoffit is a challenging problem for point pro ..."
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Cited by 85 (17 self)
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Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model’s validity prior to using it to make inferences about a particular neural system. Assessing goodnessoffit is a challenging problem for point process neural spike train models, especially for histogrambased models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The timerescaling theorem is a wellknown result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodnessoffit tests for both parametric and histogrambased point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the sup
Statistical Reconstruction And Analysis Of Autoregressive Signals In Impulsive Noise
, 1998
"... Modelling and reconstruction methods are presented for noise reduction of autocorrelated signals in nonGaussian, impulsive noise environments. A Bayesian probabilistic framework is adopted and Markov chain Monte Carlo methods are developed for detection and correction of impulses. Individual noise ..."
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Cited by 48 (16 self)
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Modelling and reconstruction methods are presented for noise reduction of autocorrelated signals in nonGaussian, impulsive noise environments. A Bayesian probabilistic framework is adopted and Markov chain Monte Carlo methods are developed for detection and correction of impulses. Individual noise sources are modelled as Gaussian with unknown scale (variance), allowing for robustness to `heavytailed' impulse distributions, while the underlying signal is modelled as autoregressive (AR). Results are presented for both artificial and real data from voice and music recordings and comparisons are made with existing techniques. The new techniques are found to give improved detection and elimination of impulses in adverse noise conditions at the expense of some extra computational complexity.
Value At Risk When Daily Changes In Market Variables Are Not Normally Distributed
 Journal of Derivatives
, 1998
"... This paper proposes a new model for calculating VaR where the user is free to choose any probability distributions for daily changes in the market variables and parameters of the probability distributions are subject to updating schemes such as GARCH. Transformations of the probability distributions ..."
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Cited by 31 (1 self)
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This paper proposes a new model for calculating VaR where the user is free to choose any probability distributions for daily changes in the market variables and parameters of the probability distributions are subject to updating schemes such as GARCH. Transformations of the probability distributions are assumed to be multivariate normal. The model is appealing in that the calculation of VaR is relatively straightforward and can make use of the RiskMetrics or a similar database. We test a version of the model using nine years of daily data on 12 different exchange rates. When the first half of the data is used to estimate the model's parameters we find that it provides a good prediction of the distribution of daily changes in the second half of the data. * Faculty of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada M5S 3E6. We are grateful to Tom McCurdy for comments and helpful suggestions. An earlier version of this paper was entitled "Taking account of the kurtosis in market variables when calculating value at risk" 2
Internet Traffic Tends To Poisson and Independent as the Load Increases
, 2001
"... The burstiness of Internet traffic was established in pioneering work in the early 1990s, which demonstrated that packet arrival times are not Poisson, and packet and byte counts in fixedlength intervals are longrange dependent [17, 20]. Here we demonstrate that these results are one end of a con ..."
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Cited by 29 (1 self)
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The burstiness of Internet traffic was established in pioneering work in the early 1990s, which demonstrated that packet arrival times are not Poisson, and packet and byte counts in fixedlength intervals are longrange dependent [17, 20]. Here we demonstrate that these results are one end of a continuum of traffic characteristics. At the other end are Poisson behavior and independence. Our study focuses on packets, what devices actually see; we study the statistical properties of packet interarrival times and packet sizes. As the traffic load increases  that is, as the number of simultaneous transport connections increases  arrivals tend to Poisson and sizes tend to independence. More specifically, longrange dependence of interarrivals and sizes decreases to independence, and the marginal distribution of interarrivals tends toward exponential; this happens (1) through time on a single link as the load increases due to daily variation, or (2) at a single point in time as the load increases going from lightly loaded links at the edges of the Internet to heavily loaded links at the core. Convergence is rapid; the packet traffic gets quite close to Poisson and independent loads far less than the maximum we observe.
Empirical bayes estimates for largescale prediction problems. http://wwwstat.stanford.edu/~ckirby/brad/papers/2008EBestimates.pdf
, 2008
"... Classical prediction methods such as Fisher’s linear discriminant function were designed for smallscale problems, where the number of predictors N is much smaller than the number of observations n. Modern scientific devices often reverse this situation. A microarray analysis, for example, might inc ..."
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Cited by 22 (4 self)
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Classical prediction methods such as Fisher’s linear discriminant function were designed for smallscale problems, where the number of predictors N is much smaller than the number of observations n. Modern scientific devices often reverse this situation. A microarray analysis, for example, might include n = 100 subjects measured on N = 10, 000 genes, each of which is a potential predictor. This paper proposes an empirical Bayes approach to largescale prediction, where the optimum Bayes prediction rule is estimated employing the data from all the predictors. Microarray examples are used to illustrate the method. The results show a close connection with the shrunken centroids algorithm of Tibshirani et al. (2002), a frequentist regularization approach to largescale prediction, and also with false discovery rate theory.
Multisensor Image Segmentation Using DempsterShafer Fusion in Markov Fields Context
 IEEE Trans. Geosci. Remote Sens
, 2001
"... This paper deals with the statistical segmentation of multisensor images. In a Bayesian context, the interest of using hidden Markov random fields, which allows one to take contextual information into account, has been well known for about 20 years. In other situations, the Bayesian framework is ins ..."
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Cited by 21 (5 self)
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This paper deals with the statistical segmentation of multisensor images. In a Bayesian context, the interest of using hidden Markov random fields, which allows one to take contextual information into account, has been well known for about 20 years. In other situations, the Bayesian framework is insufficient and one must make use of the theory of evidence. The aim of our work is to propose evidential models that can take into account contextual information via Markovian fields. We define a general evidential Markovian model and show that it is usable in practice. Different simulation results presented show the interest of evidential Markovian field modelbased segmentation algorithms. Furthermore, an original variant of generalized mixture estimation, making possible the unsupervised evidential fusion in a Markovian context, is described. It is applied to the unsupervised segmentation of real radar and SPOT images showing the relevance of the proposed models and corresponding segmentation methods in real situations.