The Experts below are selected from a list of 21729 Experts worldwide ranked by ideXlab platform
Roland Toth - One of the best experts on this subject based on the ideXlab platform.
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lpv state space model identification in the Bayesian Setting a 3 step procedure
Advances in Computing and Communications, 2016Co-Authors: P Pepijn B Cox, Roland TothAbstract:Current state-of-the-art linear parameter-varying (LPV) control design methods presume that an LPV state-space (SS) model of the system with affine dependence on the scheduling variable is available. However, many existing LPV-SS identification schemes either suffer heavily from computational issues related to the curse of dimensionality or are based on severe approximations. To overcome these issues, in this paper, the Bayesian framework is combined with a recently developed efficient SS realization scheme. We propose a computationally attractive 3-step approach for identifying LPV-SS models. In Step 1, the sub-Markov parameters representing the impulse response of the system are estimated in a Bayesian Setting, using kernel based Ridge regression with hyper-parameter tuning via marginal likelihood optimization. Subsequently, in Step 2, an LPV-SS realization is obtained by using an efficient basis reduced Ho-Kalman like deterministic SS realization scheme on the identified impulse response. Finally, in Step 3, to reach the maximum likelihood estimate, the LPV-SS model is refined by applying a Bayesian expectation-maximization method. The performance of the proposed 3-step scheme is demonstrated on a Monte-Carlo simulation study.
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ACC - LPV State-space model identification in the Bayesian Setting: A 3-step procedure
2016 American Control Conference (ACC), 2016Co-Authors: Pb Pepijn Cox, Roland TothAbstract:Current state-of-the-art linear parameter-varying (LPV) control design methods presume that an LPV state-space (SS) model of the system with affine dependence on the scheduling variable is available. However, many existing LPV-SS identification schemes either suffer heavily from computational issues related to the curse of dimensionality or are based on severe approximations. To overcome these issues, in this paper, the Bayesian framework is combined with a recently developed efficient SS realization scheme. We propose a computationally attractive 3-step approach for identifying LPV-SS models. In Step 1, the sub-Markov parameters representing the impulse response of the system are estimated in a Bayesian Setting, using kernel based Ridge regression with hyper-parameter tuning via marginal likelihood optimization. Subsequently, in Step 2, an LPV-SS realization is obtained by using an efficient basis reduced Ho-Kalman like deterministic SS realization scheme on the identified impulse response. Finally, in Step 3, to reach the maximum likelihood estimate, the LPV-SS model is refined by applying a Bayesian expectation-maximization method. The performance of the proposed 3-step scheme is demonstrated on a Monte-Carlo simulation study.
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CDC - Bayesian identification of LPV Box-Jenkins models
2015 54th IEEE Conference on Decision and Control (CDC), 2015Co-Authors: Mohamed Abdelmonim Hassan Darwish, Gianluigi Pillonetto, Pb Pepijn Cox, Roland TothAbstract:In this paper, we introduce a nonparametric approach in a Bayesian Setting to efficiently estimate, both in the stochastic and computational sense, linear parameter-varying (LPV) input-output models under general noise conditions of Box-Jenkins (BJ) type. The approach is based on the estimation of the one-step-ahead predictor model of general LPV-BJ structures, where the sub-predictors associated with the input and output signals are captured as asymptotically stable infinite impulse response models (IIRs). These IIR sub-predictors are identified in a completely nonparametric sense, where not only the coefficients are estimated as functions, but also the whole time evolution of the impulse response is estimated as a function. In this Bayesian Setting, the one-step-ahead predictor is modelled as a zero-mean Gaussian random field, where the covariance function is a multidimensional Gaussian kernel that encodes both the possible structural dependencies and the stability of the predictor. The unknown hyperparameters that parameterize the kernel are tuned using the empirical Bayes approach, i.e., optimization of the marginal likelihood with respect to available data. It is also shown that, in case the predictor has a finite order, i.e., the true system has an ARX noise structure, our approach is able to recover the underlying structural dependencies. The performance of the identification method is demonstrated on LPV-ARX and LPV-BJ simulation examples by means of a Monte Carlo study.
Arturo J Fernandez - One of the best experts on this subject based on the ideXlab platform.
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Bayesian inference from type ii doubly censored rayleigh data
Statistics & Probability Letters, 2000Co-Authors: Arturo J FernandezAbstract:In this paper we present a Bayesian approach to inference in reliability studies based on type II doubly censored data from a Rayleigh distribution. We also consider the problem of predicting an independent future sample from the same distribution in a Bayesian Setting. The results can be used to predict the failure-time of a k-out-of-m system. Bayes estimators are obtained in nice closed forms. Highest posterior density (HPD) and maximum likelihood (ML) estimators, and HPD intervals can readily be computed using iterative methods.
Pb Pepijn Cox - One of the best experts on this subject based on the ideXlab platform.
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ACC - LPV State-space model identification in the Bayesian Setting: A 3-step procedure
2016 American Control Conference (ACC), 2016Co-Authors: Pb Pepijn Cox, Roland TothAbstract:Current state-of-the-art linear parameter-varying (LPV) control design methods presume that an LPV state-space (SS) model of the system with affine dependence on the scheduling variable is available. However, many existing LPV-SS identification schemes either suffer heavily from computational issues related to the curse of dimensionality or are based on severe approximations. To overcome these issues, in this paper, the Bayesian framework is combined with a recently developed efficient SS realization scheme. We propose a computationally attractive 3-step approach for identifying LPV-SS models. In Step 1, the sub-Markov parameters representing the impulse response of the system are estimated in a Bayesian Setting, using kernel based Ridge regression with hyper-parameter tuning via marginal likelihood optimization. Subsequently, in Step 2, an LPV-SS realization is obtained by using an efficient basis reduced Ho-Kalman like deterministic SS realization scheme on the identified impulse response. Finally, in Step 3, to reach the maximum likelihood estimate, the LPV-SS model is refined by applying a Bayesian expectation-maximization method. The performance of the proposed 3-step scheme is demonstrated on a Monte-Carlo simulation study.
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CDC - Bayesian identification of LPV Box-Jenkins models
2015 54th IEEE Conference on Decision and Control (CDC), 2015Co-Authors: Mohamed Abdelmonim Hassan Darwish, Gianluigi Pillonetto, Pb Pepijn Cox, Roland TothAbstract:In this paper, we introduce a nonparametric approach in a Bayesian Setting to efficiently estimate, both in the stochastic and computational sense, linear parameter-varying (LPV) input-output models under general noise conditions of Box-Jenkins (BJ) type. The approach is based on the estimation of the one-step-ahead predictor model of general LPV-BJ structures, where the sub-predictors associated with the input and output signals are captured as asymptotically stable infinite impulse response models (IIRs). These IIR sub-predictors are identified in a completely nonparametric sense, where not only the coefficients are estimated as functions, but also the whole time evolution of the impulse response is estimated as a function. In this Bayesian Setting, the one-step-ahead predictor is modelled as a zero-mean Gaussian random field, where the covariance function is a multidimensional Gaussian kernel that encodes both the possible structural dependencies and the stability of the predictor. The unknown hyperparameters that parameterize the kernel are tuned using the empirical Bayes approach, i.e., optimization of the marginal likelihood with respect to available data. It is also shown that, in case the predictor has a finite order, i.e., the true system has an ARX noise structure, our approach is able to recover the underlying structural dependencies. The performance of the identification method is demonstrated on LPV-ARX and LPV-BJ simulation examples by means of a Monte Carlo study.
Albert C. Reynolds - One of the best experts on this subject based on the ideXlab platform.
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Quantifying Uncertainty for the PUNQ-S3 Problem in a Bayesian Setting With RML and EnKF
SPE Journal, 2006Co-Authors: Guohua Gao, Mohammad Zafari, Albert C. ReynoldsAbstract:Summary The well known PUNQ-S3 reservoir model represents a synthetic problem which was formulated to test the ability of various methods and research groups to quantify the uncertainty in the prediction of cumulative oil production. Previous results reported on this project suggest that the randomized maximum likelihood (RML) method gives a biased characterization of the uncertainty. A major objective of this paper is to show that this is incorrect. With a correct implementation of the RML method within a Bayesian framework, we show that RML does an adequate job of sampling the a posteriori distribution for the PUNQ problem. In particular, the true predicted oil production lies within the band of predictions generated with the RML method and is not biased. We also apply the ensemble Kalman Filter (EnKF) method to the PUNQ data set, and show that this method also gives a reasonable quantification of the uncertainty in performance predictions with an uncertainty range similar to the one obtained with RML. Introduction We consider conditioning models to production data in a Bayesian framework and wish to generate a suite (ensemble) of models which represent a correct sampling of the conditional probability density function (pdf). By predicting future reservoir performance with each realization, we obtain a characterization of the uncertainty in predicted performance. Both the rejection algorithm and Markov chain Monte Carlo (MCMC) are theoretically sound sampling procedures, but they are too computationally inefficient for practical applications (Liu and Oliver 2003). Oliver et al. (1996) and Kitanidis (1986) independently proposed the randomized maximum likelihood (RML) method to generate an approximate sampling of the a posteriori pdf. Two different proofs (Oliver 1996; Reynolds et al. 1999) have been presented which show that the RML method samples the posterior probability density function (pdf) correctly if data are linearly related to the model; however, no rigorous theoretical foundation exists for the method when the relation between data and model is nonlinear, which is the case when the data represent production data. Computational results indicate that the RML method generates reasonable characterization of uncertainty for single-phase flow (Oliver et al. 1996; Reynolds et al. 1999; Liu and Oliver 2003). Our first objective is to show that, contrary to a previous claim (Floris 2001), RML gives a reasonable characterization of the uncertainty in predicted performance for the PUNQ-S3 problem; our second objective is to compare the quantification of uncertainty obtained with RML with the one obtained with the ensemble Kalman filter (EnKF). The PUNQ-S3 reservoir represents a synthetic model based on an actual reservoir (Floris et al. 2001; Barker et al. 2001). The problem was set up as a test case to allow various research groups to test their own methodology for the characterization of the uncertainty in reservoir performance predictions given some geologic information on the reservoir, hard data at well gridblocks and some scattered production data from the first 8 years of production. Then participants were asked to predict cumulative oil production for 16.5 years of total production and characterize the uncertainty in this prediction.
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Quantifying Uncertainty for the PUNQ-S3 Problem in a Bayesian Setting With RML and EnKF
All Days, 2005Co-Authors: Guohua Gao, Mohammad Zafari, Albert C. ReynoldsAbstract:The well known PUNQ-S3 reservoir model represents a synthetic problem which was formulated to test the ability of various methods and research groups to quantify the uncertainty in the prediction of cumulative oil production. Previous results reported on this project suggest that the randomized maximum likelihood (RML) method gives a biased characterization of the uncertainty. A major objective of this paper is to show that this is incorrect. With a correct implementation of the RML method within a Bayesian framework, we show that RML does an adequate job of sampling the a posteriori distribution for the PUNQ problem. In particular, the true predicted oil production lies within the band of predictions generated with the RML method and is not biased. Very recently, the Ensemble Kalman Filter has gained notoriety, because it is very easy to couple with any reservoir simulator, allows one to continuously assimilate dynamic data as the forward simulation run is done and allows one to characterize uncertainty in performance predictions. When applied to the PUNQ data set, we show that this method also gives a reasonable quantification of the uncertainty in performance predictions with an uncertainty range similar to the one obtained with RML.
Reza Habibi - One of the best experts on this subject based on the ideXlab platform.
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The detection of multiple faults in a Bayesian Setting using dynamic programming approaches
Signal Processing, 2020Co-Authors: Hamed Habibi, Ian Howard, Reza HabibiAbstract:Abstract Inspired by the need for improving the reliability and safety of complex dynamic systems, this paper tackles the multiple faults detection problem using Dynamic Programming (DP) based methods under the Bayesian framework. These methods include (i) Maximum-A-Posteriori (MAP) estimator approach, (ii) Monte Carlo Markov Chain (MCMC) posteriors, (iii) Set Membership (SM) approach, (iv) probability of fault and (v) alternative methods. Using Bernoulli and Poisson priors, the Bayesian DP-type MAP estimate of all unknown parameters is presented. To derive the posterior distributions of Bayesian point estimations, the MCMC method is applied. For the SM approach, the Bayesian feasible parameter space is derived, as Bayesian confidence interval. The SM criteria are proposed to detect multiple faults which also reduces the Bayesian complexity of MAP estimator. For online fault detection, using the Bayesian model selection technique and the MAP estimator, the DP-based probability of faults is given, serving as a Bayesian early warning system. Since running DP algorithms is a time-consuming, alternative methods are also proposed using the modified MAP estimator. These methods use iterative approximations of MAP estimates, via the application of an iterative Expectation–Maximization algorithm technique. Numerical simulations are conducted and analysed to evaluate the performance of the proposed methods.
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Aggregate Portfolio Risk Approximation under Bayesian Setting
2016Co-Authors: Reza HabibiAbstract:In portfolio management, it is too important to consider non-sampling information. In this problem, the non-sampling information may be belief of investor about a special asset obtained of historical data of past economical performance of specified asset. This information forms a prior probability regard keeping the asset in portfolio or dropping it. Therefore, for each asset a binary random variable is induced to the problem which is one if the asset will be kept in portfolio and zero if it will be dropped based on investor prior belief about the asset before observing the actual risk and return. These variables are correlated come from a Dirichlet distribution. Hence, the Bayesian Setting is a suitable framework to study this problem. In this paper, the Monte Carlo method is applied to approximate the posterior distribution using Monte Carlo Markov Chain (MCMC) method of binary variables given the past returns which indicates the tendency of investor to keep or drop an asset by using the non-sampling and sampling information simultaneously. ModelRisk software is used to derive the analytical results. Bayesian CAPM and APT are proposed. Stochastic approximations are given.
