K-optimal designs for parameters of shifted Ornstein–Uhlenbeck processes and sheets

Baran, Sándor

doi:10.1016/j.jspi.2017.02.003

Cited by 5 publications

(3 citation statements)

References 25 publications

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“…The p -th order polynomial regression model is investigated, and a theoretical symmetry DoE in the space

was given in the original paper of Ye [ 13 ], where the boundary is usually included. Sándor Baran [ 14 ] extended the K-optimal to the correlated processes, i.e., Ornstein–Uhlenbeck processes, in his research. The simulation results in reference [ 14 ] show the superiority of restricted K-optimal designs for large covariance parameter values.…”

Section: Brief Reviewmentioning

confidence: 99%

“…Sándor Baran [ 14 ] extended the K-optimal to the correlated processes, i.e., Ornstein–Uhlenbeck processes, in his research. The simulation results in reference [ 14 ] show the superiority of restricted K-optimal designs for large covariance parameter values. So, the K-optimal design has potential application in deriving stable and accurate approximations.…”

Section: Brief Reviewmentioning

confidence: 99%

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Bayesian Optimization Based on K-Optimality

Yan

Duan

Liu

et al. 2018

Entropy

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Bayesian optimization (BO) based on the Gaussian process (GP) surrogate model has attracted extensive attention in the field of optimization and design of experiments (DoE). It usually faces two problems: the unstable GP prediction due to the ill-conditioned Gram matrix of the kernel and the difficulty of determining the trade-off parameter between exploitation and exploration.To solve these problems, we investigate the K-optimality, aiming at minimizing the condition number. Firstly, the Sequentially Bayesian K-optimal design (SBKO) is proposed to ensure the stability of the GP prediction, where the K-optimality is given as the acquisition function. We show that the SBKO reduces the integrated posterior variance and maximizes the hyper-parameters' information gain simultaneously. Secondly, a K-optimal enhanced Bayesian Optimization (KO-BO) approach is given for the optimization problems, where the K-optimality is used to define the trade-off balance parameters which can be output automatically. Specifically, we focus our study on the K-optimal enhanced Expected Improvement algorithm (KO-EI). Numerical examples show that the SBKO generally outperforms the Monte Carlo, Latin hypercube sampling, and sequential DoE approaches by maximizing the posterior variance with the highest precision of prediction. Furthermore, the study of the optimization problem shows that the KO-EI method beats the classical EI method due to its higher convergence rate and smaller variance.

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“…The p -th order polynomial regression model is investigated, and a theoretical symmetry DoE in the space

Section: Brief Reviewmentioning

confidence: 99%

Section: Brief Reviewmentioning

confidence: 99%

Bayesian Optimization Based on K-Optimality

Yan

Duan

Liu

et al. 2018

Entropy

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show abstract

“…The problem of theoretically finding prospective optimal designs for Ornstein-Uhlenbeck processes has been of interest to many authors for example, Kisel'ák and Stehlík (2008), Zagoraiou and Antognini (2009), Antognini and Zagoraiou (2010), , Baran et al (2013), , Baran (2017), Sikolya and Baran (2020), and Dasgupta et al (2021)). For Ornstein-Uhlenbeck (OU) processes with one-dimensional inputs, Kisel'ák and Stehlík (2008), Zagoraiou and Antognini (2009), Antognini and Zagoraiou (2010), and Dasgupta et al (2021) found optimal designs under D-optimality, D s -optimality, entropy, and integrated mean square prediction error (IMSPE) criteria.…”

Section: Introductionmentioning

confidence: 99%

G-optimal grid designs for kriging models

Dasgupta¹,

Mukhopadhyay²,

Keith³

2021

Preprint

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This work is focused on finding G-optimal designs theoretically for kriging models with two-dimensional inputs and separable exponential covariance structures. For design comparison, the notion of evenness of two-dimensional grid designs is developed. The mathematical relationship between the design and the supremum of the mean squared prediction error (SM SP E) function is studied and then optimal designs are explored for both prospective and retrospective design scenarios. In the case of prospective designs, the new design is developed before the experiment is conducted and the regularly spaced grid is shown to be the G-optimal design. The retrospective designs are constructed by adding or deleting points from an already existing design. Deterministic algorithms are developed to find the best possible retrospective designs (which minimizes the SM SP E). It is found that a more evenly spread design leads to the best possible retrospective design. For all the cases of finding the optimal prospective designs and the best possible retrospective designs, both frequentist and Bayesian frameworks have been considered. The proposed methodology for finding retrospective designs is illustrated for a methane flux monitoring design.

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D-optimal designs for complex Ornstein–Uhlenbeck processes

Baran

Szak-Kocsis

Stehlík

2018

Journal of Statistical Planning and Inference

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Complex Ornstein-Uhlenbeck (OU) processes have various applications in statistical modelling. They play role e.g. in the description of the motion of a charged test particle in a constant magnetic field or in the study of rotating waves in time-dependent reaction diffusion systems, whereas Kolmogorov used such a process to model the so-called Chandler wobble, small deviation in the Earth's axis of rotation. In these applications parameter estimation and model fitting is based on discrete observations of the underlying stochastic process, however, the accuracy of the results strongly depend on the observation points.This paper studies the properties of D-optimal designs for estimating the parameters of a complex OU process with a trend. We show that in contrast with the case of the classical real OU process, a D-optimal design exists not only for the trend parameter, but also for joint estimation of the covariance parameters, moreover, these optimal designs are equidistant.

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K-optimal designs for parameters of shifted Ornstein–Uhlenbeck processes and sheets

Cited by 5 publications

References 25 publications

Bayesian Optimization Based on K-Optimality

Bayesian Optimization Based on K-Optimality

G-optimal grid designs for kriging models

D-optimal designs for complex Ornstein–Uhlenbeck processes

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