Prediction intervals for integrals of Gaussian random fields

Oliveira, Victor De; Kone, Bazoumana

doi:10.1016/j.csda.2014.09.013

Cited by 6 publications

(2 citation statements)

References 33 publications

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“…y r P u i , P λi can be modelled as a GP, as it can be rewritten as a Riemann sum of Gaussian random variables [33]. The mean and the covariance function of y r P u i , P λi can be derived to obtain its distribution: E y r P u i ,…”

Section: Modelling Real Fuel Consumption Y R With Input Uncertaintymentioning

confidence: 99%

Ship Emission Mitigation Strategies Choice Under Uncertainty

Yuan

Wang

et al. 2020

Energies

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Various mitigation strategies have been proposed to reduce the CO2 emissions from ships, which have become a major contributor to global emissions. The fuel consumption under different mitigation strategies can be evaluated based on two data sources, real data from the real ship systems and simulated data from the simulation models. In practice, the uncertainties in the obtained data may have non-negligible impacts on the evaluation of mitigation strategies. In this paper, a Gaussian process metamodel-based approach is proposed to evaluate the ship fuel consumption under different mitigation strategies. The proposed method not only can incorporate different data sources but also consider the uncertainties in the data to obtain a more reliable evaluation. A cost-effectiveness analysis based on the fuel consumption prediction is then applied to rank the mitigation strategies under uncertainty. The accuracy and efficiency of the proposed method is illustrated in a chemical tanker case study, and the results indicate that it is critical to consider the uncertainty, as they can lead to suboptimal decisions when ignored. Here, trim optimisation is ranked more effective than draft optimisation when the uncertainty is ignored, but the reverse is the case when the uncertainty in the estimations are fully accounted for.

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Section: Modelling Real Fuel Consumption Y R With Input Uncertaintymentioning

confidence: 99%

Ship Emission Mitigation Strategies Choice Under Uncertainty

Yuan

Wang

et al. 2020

Energies

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show abstract

“…Although the prediction may not be simple, because we could not apply directly the Gaussian process theory, in this case, the problem comes back in the univariate framework and may be solved by considering the univariate conditional distribution of the summary statistics given Y = y , which can be known at least approximatively or, if necessary, estimated using simulation‐based methods. As a remarkable example, we may consider the problem of predicting the spatial average of a Gaussian random field over a subset of the region of interest Δ(see, for example, De Oliveira & Kone, ). In this case, according to the L 2 integration theory for random fields, the spatial average is a random variable defined as a stochastic integral, which can be approximated by a weighted average of (future) observations for the random field in suitable multiple locations inside the integration domain.…”

Section: Estimative Prediction Regionsmentioning

confidence: 99%

Calibrated prediction regions for Gaussian random fields

Lagazio

Vidoni

2018

Environmetrics

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This paper proposes a method to construct well‐calibrated frequentist prediction regions, with particular regard to the highest prediction density regions, which may be useful for multivariate spatial prediction. We consider, in particular, Gaussian random fields, and using a calibrating procedure we effectively improve the estimative prediction regions, because the coverage probability turns out to be closer to the target nominal value. Whenever a closed‐form expression for the well‐calibrated prediction region is not available, we may specify a simple bootstrap‐based estimator. Particular attention is dedicated to the associated, improved predictive distribution function, which can be usefully considered for identifying spatial locations with extreme or unusual observations. A simulation study is proposed in order to compare empirically the calibrated predictive regions with the estimative ones. The proposed method is then applied to the global model assessment of a deterministic model for the prediction of PM10 levels using data from a network of air quality monitoring stations.

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Gaussian process based optimization algorithms with input uncertainty

Wang

Yuan²,

2019

IISE Transactions

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Prediction intervals for integrals of Gaussian random fields

Cited by 6 publications

References 33 publications

Ship Emission Mitigation Strategies Choice Under Uncertainty

Ship Emission Mitigation Strategies Choice Under Uncertainty

Calibrated prediction regions for Gaussian random fields

Gaussian process based optimization algorithms with input uncertainty

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