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42
On the Convergence of Monte Carlo Maximum Likelihood Calculations
 Journal of the Royal Statistical Society B
, 1992
"... Monte Carlo maximum likelihood for normalized families of distributions (Geyer and Thompson, 1992) can be used for an extremely broad class of models. Given any family f h ` : ` 2 \Theta g of nonnegative integrable functions, maximum likelihood estimates in the family obtained by normalizing the the ..."
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Cited by 59 (4 self)
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Monte Carlo maximum likelihood for normalized families of distributions (Geyer and Thompson, 1992) can be used for an extremely broad class of models. Given any family f h ` : ` 2 \Theta g of nonnegative integrable functions, maximum likelihood estimates in the family obtained by normalizing the the functions to integrate to one can be approximated by Monte Carlo, the only regularity conditions being a compactification of the parameter space such that the the evaluation maps ` 7! h ` (x) remain continuous. Then with probability one the Monte Carlo approximant to the log likelihood hypoconverges to the exact log likelihood, its maximizer converges to the exact maximum likelihood estimate, approximations to profile likelihoods hypoconverge to the exact profile, and level sets of the approximate likelihood (support regions) converge to the exact sets (in Painlev'eKuratowski set convergence). The same results hold when there are missing data (Thompson and Guo, 1991, Gelfand and Carlin, 19...
Performance Engineering of the World Wide Web: Application to Dimensioning and Cache Design
, 1996
"... The quality of the service provided by the World Wide Web, namely convenient access to a tremendous amount of information in remote locations, depends in an important way on the time required to retrieve this information. This time in turn depends on a number of parameters, in particular the load at ..."
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Cited by 40 (0 self)
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The quality of the service provided by the World Wide Web, namely convenient access to a tremendous amount of information in remote locations, depends in an important way on the time required to retrieve this information. This time in turn depends on a number of parameters, in particular the load at the server and in the network. Overloads are avoided by carefully dimensioning the server (so that it has enough resources such as CPU power and disk space to handle expected requests) and the network (so that it has enough resources such as bandwidth and buoeers to transport requests and replies), and by using mechanisms such as caching that minimize the resource requirements of user requests. In this paper, we consider performance issues related to dimensioning and caching. Our contribution is twofold. Regarding dimensioning, we advocate the use of time series analysis techniques for Web traffic modeling and forecasting. We show using experimental data that quantities of interest such as t...
On the Applicability of Regenerative Simulation in Markov Chain Monte Carlo
, 2001
"... We consider the central limit theorem and the calculation of asymptotic standard errors for the ergodic averages constructed in Markov chain Monte Carlo. Chan & Geyer (1994) established a central limit theorem for ergodic averages by assuming that the underlying Markov chain is geometrically ..."
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Cited by 32 (21 self)
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We consider the central limit theorem and the calculation of asymptotic standard errors for the ergodic averages constructed in Markov chain Monte Carlo. Chan & Geyer (1994) established a central limit theorem for ergodic averages by assuming that the underlying Markov chain is geometrically ergodic and that a simple moment condition is satisfied. While it is relatively straightforward to check Chan and Geyer's conditions, their theorem does not lead to a consistent and easily computed estimate of the variance of the asymptotic normal distribution. Conversely, Mykland, Tierney & Yu (1995) discuss the use of regeneration to establish an alternative central limit theorem with the advantage that a simple, consistent estimate of the asymptotic variance is readily available. However, their result assumes a pair of unwieldy moment conditions whose verification is difficult in practice. In this paper, we show that the conditions of Chan and Geyer's theorem are sucient to establish Mykland, Tierney, and Yu's central limit theorem. This result, in conjunction with other recent developments, should pave the way for more widespread use of the regenerative method in Markov chain Monte Carlo. Our results are applied to the slice sampler for illustration.
Methods for quantifying the causal structure of bivariate time series
 Int. J. of Bifurcation and Chaos
, 2006
"... In the study of complex systems one of the major concerns is the detection and characterization of causal interdependencies and couplings between different subsystems. The nature of such dependencies is typically not only nonlinear but also asymmetric and thus makes the use of symmetric and linear m ..."
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Cited by 8 (1 self)
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In the study of complex systems one of the major concerns is the detection and characterization of causal interdependencies and couplings between different subsystems. The nature of such dependencies is typically not only nonlinear but also asymmetric and thus makes the use of symmetric and linear methods ineffective. Moreover, signals sampled from real world systems are noisy and short, posing additional constraints on the estimation of the underlying couplings. In this article, we compare a set of six recently introduced methods for quantifying the causal structure of bivariate time series extracted from systems with complex dynamical behavior. We discuss the usefulness of the methods for detecting asymmetric couplings and directional flow of information in the context of uni and bidirectionally coupled deterministic chaotic systems. Key words: causal structure, nonlinear time series analysis, coupled systems, information flow
Discriminating Mental Tasks Using EEG Represented by AR Models
 In Proceedings of the 1995 IEEE Engineering in Medicine and Biology Annual Conference
, 1995
"... EEG signals are modeled using singlechannel and multichannel autoregressive (AR) techniques. The coefficients of these models are used to classify EEG data into one of two classes corresponding to the mental task the subjects are performing. A neural network is trained to perform the classificatio ..."
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Cited by 6 (0 self)
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EEG signals are modeled using singlechannel and multichannel autoregressive (AR) techniques. The coefficients of these models are used to classify EEG data into one of two classes corresponding to the mental task the subjects are performing. A neural network is trained to perform the classification. When applying a trained network to test data, we find that the multivariate AR representation performs slightly better, resulting in an average classification accuracy of about 91%. I. Introduction and Background If different mental states can be reliably detected solely on the basis of EEG, then a new means of communication for paralyzed persons can be developed with which, for example, a wheelchair could be controlled. This difficult pattern recognition problem is primarily one finding a signal representation that captures information related to the mental state of a person in a way that is invariant to time and subject. This paper describes the results of experiments that were perfor...
Estimation and Interpretation of 1/f α Noise in human cognition
, 2003
"... Recent analyses of serial correlations in cognitive tasks have provided preliminary evidence for the presence of a particular form of longrange serial dependence known as 1/f noise. It has been argued that longrange dependence has been largely ignored by mainstream cognitive psychology even though ..."
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Cited by 6 (1 self)
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Recent analyses of serial correlations in cognitive tasks have provided preliminary evidence for the presence of a particular form of longrange serial dependence known as 1/f noise. It has been argued that longrange dependence has been largely ignored by mainstream cognitive psychology even though it accounts for a substantial proportion of variability in behavior (e.g., Gilden, 1997, 2001). In this article, we discuss the defining characteristics of longrange dependence and argue that claims about its presence need to be evaluated by testing against the alternative hypothesis of shortrange dependence. For the data from three experiments, we accomplish such tests with autoregressive fractionallyintegrated moving average time series modeling. We find that longrange serial dependence in these experiments can be explained by any of several mechanisms, including mixtures of a small number of shortrange processes.
Control Relevant Identification of a Compact Disc Pickup Mechanism
, 1993
"... This paper discusses the control relevant parametric identification of a servo system present in a Compact Disc player. In this application an approximate closed loop identification problem is... ..."
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Cited by 3 (0 self)
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This paper discusses the control relevant parametric identification of a servo system present in a Compact Disc player. In this application an approximate closed loop identification problem is...
Timefrequency spectral estimation of multichannel EEG using the autoSLEX method
 IEEE Transactions on Biomedical Engineering
, 2002
"... Abstract—In this paper, we apply a new timefrequency spectral estimation method for multichannel data to epileptiform electroencephalography (EEG). The method is based on the smooth localized complex exponentials (SLEX) functions which are timefrequency localized versions of the Fourier functions ..."
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Cited by 3 (0 self)
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Abstract—In this paper, we apply a new timefrequency spectral estimation method for multichannel data to epileptiform electroencephalography (EEG). The method is based on the smooth localized complex exponentials (SLEX) functions which are timefrequency localized versions of the Fourier functions and, hence, are ideal for analyzing nonstationary signals whose spectral properties evolve over time. The SLEX functions are simultaneously orthogonal and localized in time and frequency because they are obtained by applying a projection operator rather than a window or taper. In this paper, we present the AutoSLEX method which is a statistical method that 1) computes the periodogram using the SLEX transform, 2) automatically segments the signal into approximately stationary segments using an objective criterion that is based on log energy, and 3) automatically selects the optimal bandwidth of the spectral smoothing window. The method is applied to the intracranial EEG from a patient with temporal lobe epilepsy. This analysis reveals a reduction in average duration of stationarity in preseizure epochs of data compared to baseline. These changes begin up to hours prior to electrical seizure onset in this patient. Index Terms—Electroencephalography, spectral analysis, stochastic processes, timefrequency analysis. I.
conditions on realizable twopoint correlation functions of random media
, 2009
"... A fascinating inverse problem that has been receiving considerable attention is the construction of realizations of random twophase heterogeneous media with a target twopoint correlation function. However, not every hypothetical twopoint correlation function corresponds to a realizable twophase ..."
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Cited by 2 (2 self)
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A fascinating inverse problem that has been receiving considerable attention is the construction of realizations of random twophase heterogeneous media with a target twopoint correlation function. However, not every hypothetical twopoint correlation function corresponds to a realizable twophase medium. Here we collect all of the known necessary conditions on the twopoint correlation functions scattered throughout a diverse literature and derive a new but simple positivity condition. We apply the necessary conditions to test the realizability of certain classes of proposed correlation functions. 1