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540
Convergence rates of posterior distributions
 Ann. Statist
, 2000
"... We consider the asymptotic behavior of posterior distributions and Bayes estimators for infinitedimensional statistical models. We give general results on the rate of convergence of the posterior measure. These are applied to several examples, including priors on finite sieves, logspline models, D ..."
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Cited by 43 (11 self)
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We consider the asymptotic behavior of posterior distributions and Bayes estimators for infinitedimensional statistical models. We give general results on the rate of convergence of the posterior measure. These are applied to several examples, including priors on finite sieves, logspline models, Dirichlet processes and interval censoring. 1. Introduction. Suppose
Beyond independent components: trees and clusters
 Journal of Machine Learning Research
, 2003
"... We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a treestructured graphical model. This treedependent component analysi ..."
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Cited by 42 (0 self)
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We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a treestructured graphical model. This treedependent component analysis (TCA) provides a tractable and flexible approach to weakening the assumption of independence in ICA. In particular, TCA allows the underlying graph to have multiple connected components, and thus the method is able to find “clusters ” of components such that components are dependent within a cluster and independent between clusters. Finally, we make use of a notion of graphical models for time series due to Brillinger (1996) to extend these ideas to the temporal setting. In particular, we are able to fit models that incorporate treestructured dependencies among multiple time series.
Probabilistic Adaptive Direct Optimism Control in Time Warp
 In Proceedings of the 9th Workshop on Parallel and Distributed Simulation
, 1995
"... In a distributed memory environment the communication overhead of Time Warp as induced by the rollback procedure due to "overoptimistic" progression of the simulation is the dominating performance factor. To limit optimism to an extent that can be justified from the inherent model parallelism, an op ..."
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Cited by 41 (5 self)
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In a distributed memory environment the communication overhead of Time Warp as induced by the rollback procedure due to "overoptimistic" progression of the simulation is the dominating performance factor. To limit optimism to an extent that can be justified from the inherent model parallelism, an optimism control mechanism is proposed, which by maintaining a history record of virtual time differences from the time stamps carried by arriving messages, and forecasting the timestamps of forthcoming messages, probabilistically delays the execution of scheduled events to avoid potential rollback and associated communication overhead (antimessages). After investigating statistical forecast methods which express only the central tendency of the arrival process, we demonstrate that arrival processes in the context of Time Warp simulations of timed Petri nets have certain predictable and consistent ARIMA characteristics, which encourage the use of sophisticated and recursive forecast procedures...
On Estimating the Intensity of LongRange Dependence in Finite and Infinite Variance Time Series
, 1996
"... The goal of this paper is to provide benchmarks to the practitioner for measuring the intensity of longrange dependence in time series. It provides a detailed comparison of eight estimators for longrange dependence, using simulated FARIMA(p; d; q) time series with different finite and infinite var ..."
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Cited by 41 (3 self)
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The goal of this paper is to provide benchmarks to the practitioner for measuring the intensity of longrange dependence in time series. It provides a detailed comparison of eight estimators for longrange dependence, using simulated FARIMA(p; d; q) time series with different finite and infinite variance innovations. FARIMA time series model both longrange dependence (through the parameter d) and shortrange dependence (through the parameters p and q). We evaluate the biases and standard deviations of several estimators of d and compare them for each type of series used. We consider Gaussian, exponential, lognormal, Pareto, symmetric and skewed stable innovations. Detailed tables and graphs have been included. We find that the estimators tend to perform less well when p and q are not zero, that is, when there is additional shortrange dependence structure. For most of the estimators, however, the use of infinite variance instead of finite variance innovations does not cause a great dec...
The Supremum of a Negative Drift Random Walk with Dependent HeavyTailed Steps
, 1998
"... . Many important probabilistic models in queuing theory, insurance and finance deal with partial sums of a negative mean stationary process (a negative drift random walk), and the law of the supremum of such a process is used to calculate, depending on the context, the ruin probability, the steady s ..."
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Cited by 39 (25 self)
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. Many important probabilistic models in queuing theory, insurance and finance deal with partial sums of a negative mean stationary process (a negative drift random walk), and the law of the supremum of such a process is used to calculate, depending on the context, the ruin probability, the steady state distribution of the number of customers in the system or the value at risk. When the stationary process is heavytailed, the corresponding ruin probabilities are high and the stationary distributions are heavytailed as well. If the steps of the random walk are independent, then the exact asymptotic behavior of such probability tails was described by Embrechts and Veraverbeke (1982). We show that this asymptotic behavior may be different if the steps of the random walk are not independent, and the dependence affects the joint probability tails of the stationary process. Such type of dependence can be modeled, for example, by a linear process. 1. Introduction In various applied fields...
Automatic BlockLength Selection for the Dependent Bootstrap
 Econometric Reviews
, 2004
"... We review the different block bootstrap methods for time series, and present them in a unified framework. We then revisit a recent result of Lahiri [Lahiri, S. N. (1999b). Theoretical comparisons of block bootstrap methods, Ann. Statist. ..."
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Cited by 34 (4 self)
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We review the different block bootstrap methods for time series, and present them in a unified framework. We then revisit a recent result of Lahiri [Lahiri, S. N. (1999b). Theoretical comparisons of block bootstrap methods, Ann. Statist.
Adaptive, handsoff stream mining
 In VLDB
, 2003
"... Sensor devices and embedded processors are becoming ubiquitous, especially in measurement and monitoring applications. Automatic discovery of patterns and trends in the large volumes of such data is of paramount importance. The combination of relatively limited resources (CPU, memory and/or communic ..."
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Cited by 32 (3 self)
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Sensor devices and embedded processors are becoming ubiquitous, especially in measurement and monitoring applications. Automatic discovery of patterns and trends in the large volumes of such data is of paramount importance. The combination of relatively limited resources (CPU, memory and/or communication bandwidth and power) poses some interesting challenges. We need both powerful and concise “languages ” to represent the important features of the data, which can (a) adapt and handle arbitrary periodic components, including bursts, and (b) require little memory and a single pass over the data. This allows sensors to automatically (a) discover interesting patterns and trends in the data, and (b) perform outlier detection to alert users. We need a way so that a sensor can discover something like “the hourly phone call volume so far follows a daily and a weekly periodicity, with bursts roughly every year, ” which a human might recognize as, e.g., the Mother’s day surge. When possible and if desired, the user can then issue explicit queries to further investigate the reported patterns. In this work we propose AWSOM (Arbitrary Window Stream mOdeling Method), which allows sensors operating in remote or hostile environments to discover patterns efficiently and
Nonparametric time series prediction through adaptive model selection
 Machine Learning
, 2000
"... Abstract. We consider the problem of onestep ahead prediction for time series generated by an underlying stationary stochastic process obeying the condition of absolute regularity, describing the mixing nature of process. We make use of recent results from the theory of empirical processes, and ada ..."
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Cited by 28 (0 self)
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Abstract. We consider the problem of onestep ahead prediction for time series generated by an underlying stationary stochastic process obeying the condition of absolute regularity, describing the mixing nature of process. We make use of recent results from the theory of empirical processes, and adapt the uniform convergence framework of Vapnik and Chervonenkis to the problem of time series prediction, obtaining finite sample bounds. Furthermore, by allowing both the model complexity and memory size to be adaptively determined by the data, we derive nonparametric rates of convergence through an extension of the method of structural risk minimization suggested by Vapnik. All our results are derived for general L p error measures, and apply to both exponentially and algebraically mixing processes.
Joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a Bayesian sampling approach
 IEEE Transactions on Signal Processing
, 2007
"... We propose a joint segmentation algorithm for piecewise constant AR processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors allow to introduce correlations between the change locations of the observed signals. Numerical problems ..."
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Cited by 28 (16 self)
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We propose a joint segmentation algorithm for piecewise constant AR processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors allow to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint segmentation methodology provides interesting results compared to a signalbysignal segmentation. 1.