On Prediction Properties of Kriging: Uniform Error Bounds and Robustness

Wang, Wenjia; Tuo, Rui; Wu, Changbao

doi:10.1080/01621459.2019.1598868

Cited by 45 publications

(55 citation statements)

References 27 publications

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“…This threshold choice is a model design choice, however, we found from our experiments that predictive scores above 0.1 often yield satisfactory estimates in practice. This choice was also reported in [50]. Our model predictive score is 0.4656, which passes the model checking.…”

Section: Model Predictive Checkingsupporting

confidence: 62%

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Anomaly Detection System for Water Networks in Northern Ethiopia Using Bayesian Inference

Tashman

Gorder²,

Parthasarathy

et al. 2020

Sustainability

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For billions of people living in remote and rural communities in the developing countries, small water systems are the only source of clean drinking water. Due to the rural nature of such water systems, site visits may occur infrequently. This means broken water systems can remain in a malfunctioning state for months, forcing communities to return to drinking unsafe water. In this work, we present a novel two-level anomaly detection system aimed to detect malfunctioning remote sensored water hand-pumps, allowing for a proactive approach to pump maintenance. To detect anomalies, we need a model of normal water usage behavior first. We train a multilevel probabilistic model of normal usage using approximate variational Bayesian inference to obtain a conditional probability distribution over the hourly water usage data. We then use this conditional distribution to construct a level-1 scoring function for each hourly water observation and a level-2 scoring function for each pump. Probabilistic models and Bayesian inference collectively were chosen for their ability to capture the high temporal variability in the water usage data at the individual pump level as well as their ability to estimate interpretable model parameters. Experimental results in this work have demonstrated that the pump scoring function is able to detect malfunctioning sensors as well as a change in water usage behavior allowing for a more responsive and proactive pump system maintenance.

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Section: Model Predictive Checkingsupporting

confidence: 62%

“…Figure 8 illustrates the predictive check on a held-out pump. The predictive checking procedure described is discussed in details in [50].…”

Section: Model Predictive Checkingmentioning

confidence: 99%

Anomaly Detection System for Water Networks in Northern Ethiopia Using Bayesian Inference

Tashman

Gorder²,

Parthasarathy

et al. 2020

Sustainability

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show abstract

“…Thus, the difference between

and ABOI(N,M) is bounded by the maximum interpolation error among all the m positions of grid M . Wang et al [ 50 ] provided an exhaustive analysis regarding this maximum interpolation error of OK. Indeed, hypothesis

allows the use of Corollary 1 of Wang et al [ 50 ] along with Theorem 11.22 of Wendland [ 51 ] to obtain the following result (a detailed description of this outcome is provided in Appendix A ):

or equivalently, for all

, there exists a

such that

…”

Section: Mathematical Foundation For the Use Of The Aboi Methodsmentioning

confidence: 99%

Improving Signal-Strength Aggregation for Mobile Crowdsourcing Scenarios

Madariaga

Bustos-Jiménez

et al. 2021

Sensors

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Due to its huge impact on the overall quality of service (QoS) of wireless networks, both academic and industrial research have actively focused on analyzing the received signal strength in areas of particular interest. In this paper, we propose the improvement of signal-strength aggregation with a special focus on Mobile Crowdsourcing scenarios by avoiding common issues related to the mishandling of log-scaled signal values, and by the proposal of a novel aggregation method based on interpolation. Our paper presents two clear contributions. First, we discuss the misuse of log-scaled signal-strength values, which is a persistent problem within the mobile computing community. We present the physical and mathematical formalities on how signal-strength values must be handled in a scientific environment. Second, we present a solution to the difficulties of aggregating signal strength in Mobile Crowdsourcing scenarios, as a low number of measurements and nonuniformity in spatial distribution. Our proposed method obtained consistently lower Root Mean Squared Error (RMSE) values than other commonly used methods at estimating the expected value of signal strength over an area. Both contributions of this paper are important for several recent pieces of research that characterize signal strength for an area of interest.

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“…Some numerical examples for the one-dimensional Poisson equation are given in Section 5. The proofs of these results are based on reproducing kernel Hilbert space (RKHS) techniques which are commonly used to analyse approximation properties of GPs (van der Vaart and van Zanten, 2011;Cialenco et al, 2012;Cockayne et al, 2017;Karvonen et al, 2020;Teckentrup, 2020;Wang et al, 2020;Wynne et al, 2021). Our central tool is Theorem 3.7, which describes the RKHS associated to the prior u GP under the assumptions that the RKHS for f GP is a Sobolev space and L is a second-order elliptic differential operator.…”

Section: Contributionsmentioning

confidence: 99%

Error analysis for a statistical finite element method

Karvonen¹,

Cirak²

2022

Preprint

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The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the true system response. We provide a probabilistic error analysis for a prototypical statFEM setup based on a Gaussian process prior under the assumption that the noisy measurement data are generated by a deterministic true system response function that satisfies a second-order elliptic partial differential equation for an unknown true source term. In certain cases, properties such as the smoothness of the source term may be misspecified by the Gaussian process model. The error estimates we derive are for the expectation with respect to the measurement noise of the L 2 -norm of the difference between the true system response and the mean of the statFEM posterior. The estimates imply polynomial rates of convergence in the numbers of measurement points and finite element basis functions and depend on the Sobolev smoothness of the true source term and the Gaussian process model. A numerical example for Poisson's equation is used to illustrate these theoretical results.

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On Prediction Properties of Kriging: Uniform Error Bounds and Robustness

Cited by 45 publications

References 27 publications

Anomaly Detection System for Water Networks in Northern Ethiopia Using Bayesian Inference

Anomaly Detection System for Water Networks in Northern Ethiopia Using Bayesian Inference

Improving Signal-Strength Aggregation for Mobile Crowdsourcing Scenarios

Error analysis for a statistical finite element method

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