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Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these surrogates. However, surrogate methods with dimension reduction generally rely on complete output training data. This article proposes a new Gaussian process surrogate method that permits the use of partially observed output while remaining computationally efficient. The new method involves the imputation of missing values and the adjustment of the covariance matrix used for Gaussian process inference. The resulting surrogate represents the available responses, disregards the missing responses, and provides meaningful uncertainty quantification. The proposed approach is shown to offer sharper inference than alternatives in a simulation study and a case study where an energy density functional model that frequently returns incomplete output is calibrated.

Functional Data Analysis (FDA) has emerged as a powerful framework for datasets that exhibit continuous variation over specified intervals. Unlike traditional methods, FDA treats data as functions, providing a more comprehensive understanding of their behavior and variability. This approach is particularly beneficial for exploring observations collected over time or space. The Spatial Functional Data Analysis (SFDA) incorporates spatial locations as an additional dimension. This integration enhances the ability to model complex associations between curves in the functional domain. Despite progress in analyzing multivariate spatial data, limited attention has been given to SFDA. This study addresses this gap by proposing a Bayesian Gaussian functional approach based on B-splines. The proposal also addresses challenges posed by irregularly spaced observations in the functional domain, a feature rarely considered in the literature. A simulation study is developed to evaluate performance. Finally, results are explored using a relatively novel real dataset from monitoring stations of temperature in Mexico City. [ABSTRACT FROM AUTHOR]

Gaussian processes are popular in spatial statistics, data mining and machine learning because of their versatility in quantifying spatial variability and in propagating uncertainty. Although there has been a prolific research activity about Gaussian processes over Euclidean domains, only recently this research has extended to non-Euclidean manifolds. This paper digs into vector-valued Gaussian processes defined over the product of a hypersphere and a Euclidean space of arbitrary dimension, which are of interest in various disciplines of the natural sciences and engineering. Under mild regularity conditions, we establish a surprising one-to-one correspondence between matrix-valued kernels associated with vector Gaussian processes over the product space, and what we term partial ultraspherical and Fourier transforms that are taken over either the sphere or the Euclidean subspace. The properties of our approach are illustrated in terms of new parametric classes of matrix-valued kernels for product spaces of a hypersphere crossed with a Euclidean space. We also provide two algorithms that allow for fast simulation of approximately Gaussian (in the sense of the central limit theorem) processes in such product spaces. [ABSTRACT FROM AUTHOR]

Two-sample location-scale refers to a model that permits a pair of standardised random variables to have a common base distribution. Function-based hypothesis testing in these models refers to formal tests based on distributions functions, or direct transformations thereof, that would help decide whether or not two samples come from some location-scale family of distributions. For uncensored data, an approach of testing based on plug-in empirical likelihood (PEL) is carried out with sample means and standard deviations as the plug-ins. The method extends to censored data, where censoring adjusted moment estimators provide the requisite plug-ins. The large sample null distribution of the PEL statistic is derived. Since it is not distribution free, a two-sample location-scale appropriate resampling is employed to obtain thresholds needed for the testing. Numerical studies are carried out to investigate the performance of the proposed method. Real examples are presented for both the uncensored and censored cases. [ABSTRACT FROM AUTHOR]

We discuss nonparametric estimation of the trend coefficient in models governed by a stochastic differential equation driven by a Gaussian process with small noise. [ABSTRACT FROM AUTHOR]

We consider the construction of confidence bands for survival curves under the outcome‐dependent stratified sampling. A main challenge of this design is that data are a biased dependent sample due to stratification and sampling without replacement. Most literature on regression approximates this design by Bernoulli sampling but variance is generally overestimated. Even with this approximation, the limiting distribution of the inverse probability weighted Kaplan–Meier estimator involves a general Gaussian process, and hence quantiles of its supremum is not analytically available. In this paper, we provide a rigorous asymptotic theory for the weighted Kaplan–Meier estimator accounting for dependence in the sample. We propose the novel hybrid method to both simulate and bootstrap parts of the limiting process to compute confidence bands with asymptotically correct coverage probability. Simulation study indicates that the proposed bands are appropriate for practical use. A Wilms tumor example is presented. [ABSTRACT FROM AUTHOR]

We consider an ordinary differential equation driven by rough paths, in the T. Lyons sense (Rev Mat Iberoamer. 1998;14(2)215–310), depending on a small parameter and with a negative long-range random coefficient. We establish sufficient conditions under which the solution of this ordinary differential equation converges to the solution of a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H ∈ (1 4 , 1 2) , depends on the asymptotic behavior of the covariance function of the random coefficient. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge of data-driven control of nonlinear systems, focusing on the limitations and capabilities of model reference Gaussian process regression (MR-GPR) and its evolved counterpart, model reference neural networks (MR-NN). MR-GPR, based on Gaussian processes renowned for their adaptability to diverse data structures, encounters scalability issues especially when handling large datasets. To address these limitations, this paper introduces MR-NN, an extension of MR-GPR, leveraging neural networks (NN) to manage large datasets and capture complex nonlinear dynamics effectively. We present a comprehensive evaluation of both methods through a classical control problem of the inverted pendulum, a system well-recognized for its nonlinear behavior. Numerical experiments are conducted to compare the methods in terms of control performance, computational efficiency, and reliability. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the sojourn times of conditionally Gaussian processes, i.e., the sojourns of ξ (t) + λ - ζ t β and ξ (t) (λ - ζ t β) , t ∈ [ 0 , T ] , T > 0 , where ξ is a Gaussian zero-mean stationary process and λ and ζ are random variables independent of ξ (·) , and β > 0 is a constant. [ABSTRACT FROM AUTHOR]

Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient‐enhanced covariance matrix can be beneficial since it provides a more accurate surrogate relative to its gradient‐free counterpart. An acute problem for Gaussian processes, particularly those that use gradients, is the ill‐conditioning of their covariance matrices. Several methods have been developed to address this problem for gradient‐enhanced Gaussian processes but they have various drawbacks such as limiting the data that can be used, imposing a minimum distance between evaluation points in the parameter space, or constraining the hyperparameters. In this paper a diagonal preconditioner is applied to the covariance matrix along with a modest nugget to ensure that the condition number of the covariance matrix is bounded, while avoiding the drawbacks listed above. The method can be applied with any twice‐differentiable kernel and when there are noisy function and gradient evaluations. Optimization results for a gradient‐enhanced Bayesian optimizer with the Gaussian kernel are compared with the use of the preconditioning method, a baseline method that constrains the hyperparameters, and a rescaling method that increases the distance between evaluation points. The Bayesian optimizer with the preconditioning method converges the optimality, that is, the ℓ2$$ {\ell}_2 $$ norm of the gradient, an additional 5 to 9 orders of magnitude relative to when the baseline method is used and it does so in fewer iterations than with the rescaling method. The preconditioning method is available in the open source Python library GpGradPy, which can be found at https://github.com/marchildon/gpgradpy/tree/paper_precon. [ABSTRACT FROM AUTHOR]

Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a collection of variables and functions, some of which are unknown, indexed by the nodes and hyperedges of a hypergraph (a generalized graph where edges can connect more than two vertices). Given partial observations of the variables of the hypergraph (satisfying the functional dependencies imposed by its structure), approximate all the unobserved variables and unknown functions. Type 3: Expanding on Type 2, if the hypergraph structure itself is unknown, use partial observations of the variables of the hypergraph to discover its structure and approximate its unknown functions. These hypergraphs offer a natural platform for organizing, communicating, and processing computational knowledge. While most scientific problems can be framed as the data-driven discovery of unknown functions in a computational hypergraph whose structure is known (Type 2), many require the data-driven discovery of the structure (connectivity) of the hypergraph itself (Type 3). We introduce an interpretable Gaussian Process (GP) framework for such (Type 3) problems that does not require randomization of the data, access to or control over its sampling, or sparsity of the unknown functions in a known or learned basis. Its polynomial complexity, which contrasts sharply with the super-exponential complexity of causal inference methods, is enabled by the nonlinear ANOVA capabilities of GPs used as a sensing mechanism. [ABSTRACT FROM AUTHOR]

The microstrip devices based on multimode resonators represent a class of electromagnetic microwave devices, promising use in tropospheric communication, radar, and navigation systems. The design of wideband bandpass filters, diplexers, and multiplexers with required frequency-selective properties, i.e., bandpass filters, is a complex problem, as electrodynamic modeling is a time-consuming and computationally intensive process. Various planar microstrip resonator topologies can be developed, differing in their topology type, and the search for high-quality structures with unique frequency-selective properties is an important research direction. In this study, we propose an approach for performing an automated search for multimode resonators' conductor topology parameters using a combination of evolutionary computation approach and surrogate modeling. In particular, a variant of differential evolution optimizer is applied, and the model of the target function landscape is built using Gaussian processes. At every iteration of the algorithm, the model is used to search for new high-quality solutions. In addition, a general approach for target function formulation is presented and applied in the proposed approach. The experiments with two microwave filters have demonstrated that the proposed algorithm is capable of solving the problem of tuning two types of topologies, namely three-mode resonators and six-mode resonators, to the required parameters, and the application of surrogated-assisted algorithm has significantly improved overall performance. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Bayesian Optimization (BO)-based strategy using the Gaussian Process (GP) for feature detection of a known but non-cooperative space object by a chaser with a monocular camera and a single-beam LIDAR in a close-proximity operation. Specifically, the objective of the proposed Space Object Chaser-Resident Assessment Feature Tracking (SOCRAFT) algorithm is to determine the camera directional angles so that the maximum number of features within the camera range is detected while the chaser moves in a predefined orbit around the target. For the chaser-object spatial incentive, rewards are assigned to the chaser states from a combined model with two components: feature detection score and sinusoidal reward. To calculate the sinusoidal reward, estimated feature locations are required, which are predicted by Gaussian Process models. Another Gaussian Process model provides the reward distribution, which is then used by the Bayesian Optimization to determine the camera directional angles. Simulations are conducted in both 2D and 3D domains. The results demonstrate that SOCRAFT can generally detect the maximum number of features within the limited camera range and field of view. [ABSTRACT FROM AUTHOR]

Latent factor models can perform spatio-temporal forecasting (i.e., predicting future responses at unmeasured as well as measured locations) by modeling temporal dependence using latent factors and considering spatial dependence using a spatial prior on factor loadings. However, they may fail to capture complex spatio-temporal dependence because the latent factors are typically assumed to follow a classical linear time series model, such as a vector autoregressive model. In this article, we propose a deep latent factor model for spatio-temporal forecasting that can model complex spatio-temporal dependence more flexibly by leveraging the high expressive power of a deep neural network. Specifically, the latent factors are modeled using a recurrent neural network and the factor loadings are modeled using a distance-based Gaussian process. The proposed model allows the number of latent factors to be inferred from the data using a beta-Bernoulli process, which enables computationally more efficient implementation compared to previous methods. We derive a stochastic variational inference algorithm for scalable inference of the proposed model and validate the model using simulated and real data examples. [ABSTRACT FROM AUTHOR]

Deep learning methods have been widely used in applications of yield estimation using remote sensing data. However, they still face some challenges in terms of accuracy due to their inability to fully utilize the spatiotemporal information of remote sensing data. In response to this problem, a winter wheat yield estimation method based on ensemble deep learning and Gaussian process (GP) was proposed. First, the long-short term memory (LSTM) network and convolutional neural network (CNN) were constructed to explore deep spatiotemporal features from Sentinel-1A time-series images. Then, a GP component was applied for fusion of intraimage deep spatiotemporal features and inter-sample spatial consistency features. Finally, the yield estimation results were obtained. The experimental results showed that the proposed method had higher accuracy than those compared models, with a coefficient of determination (${R^2}$ R 2 ) of 0.698, a root mean square error (RMSE) of 477.045 kg/ha and a mean absolute error (MAE) of 404.377 kg/ha, demonstrating the application potential of the proposed method in crop yield estimation applications. [ABSTRACT FROM AUTHOR]

Many techniques have been proposed to model space-varying observation processes with a nonstationary spatial covariance structure and/or anisotropy, usually on a geostatistical framework. Nevertheless, there is an increasing interest in point process applications, and methodologies that take nonstationarity into account are welcomed. In this sense, this work proposes an extension of a class of spatial Cox process using spatial deformation. The proposed method enables the deformation behavior to be data-driven, through a multivariate latent Gaussian process. Inference leads to intractable posterior distributions that are approximated via MCMC. The convergence of algorithms based on the Metropolis–Hastings steps proved to be slow, and the computational efficiency of the Bayesian updating scheme was improved by adopting Hamiltonian Monte Carlo (HMC) methods. Our proposal was also compared against an alternative anisotropic formulation. Studies based on synthetic data provided empirical evidence of the benefit brought by the adoption of nonstationarity through our anisotropic structure. A real data application was conducted on the spatial spread of the Spodoptera frugiperda pest in a corn-producing agricultural area in southern Brazil. Once again, the proposed method demonstrated its benefit over alternatives. [ABSTRACT FROM AUTHOR]

We present contrast information, a novel application of some specific cases of relative entropy, designed to be useful for the cognitive modelling of the sequential perception of continuous signals. We explain the relevance of entropy in the cognitive modelling of sequential phenomena such as music and language. Then, as a first step to demonstrating the utility of constrast information for this purpose, we empirically show that its discrete case correlates well with existing successful cognitive models in the literature. We explain some interesting properties of constrast information. Finally, we propose future work toward a cognitive architecture that uses it. [ABSTRACT FROM AUTHOR]

Concern about air-quality in urban areas has led to the implementation of Low Emission Zones as one of many other initiatives to control it. Recently in Spain, the enactment of a law made this mandatory for cities with a population larger than 50k inhabitants. The delimitation of these areas is not without controversy because of possible negative economic and social impacts. Therefore, clear assessments of how these initiatives decrease pollutant concentrations are to be provided. Madrid Central is a major initiative of Madrid city council for reducing motor traffic and the associated air pollution in the city centre. This Low Emission Zone starts at the end of 2018, but the first fully-operational period corresponds to the second quarter of 2019. In this work, a methodology based on the Gaussian Process to analyse the evolution of Nitrogen Dioxide inside Madrid Central is undertaken. A Gaussian Process is a stochastic process suitable for interpretable model selection and predictions. Due to its probabilistic nature it provides error estimation at predictions. After the activation of Madrid Central, a relevant reduction of Nitrogen Dioxide has been observed. However, the role of the meteorology during this period must be ascertained to correctly evaluate the role of the activation of the Low Emission Zone against a prone weather. In this work, a model based on the Gaussian Process is trained with meteorological information to predict the concentration of Nitrogen Dioxide at Madrid Central, |$[NO_{2}]$|⁠. This probabilistic description allows extracting statistical information on the reduction affected by the meteorological scenario and separately by the Madrid Central activation. [ABSTRACT FROM AUTHOR]

The perception system plays a crucial role by integrating LiDAR and various sensors to perform localization and object detection, which ensures the security of intelligent driving. However, existing research indicates that LiDAR is vulnerable to sensor attacks, which lead to inappropriate driving strategies and need effective attack recognition methods. Previous LiDAR attack recognition methods rely on fixed anomaly thresholds obtained from depth map data distributions in specific scenarios as static anomaly boundaries, which lead to reduced accuracy, increased false alarm rates, and a lack of performance stability. To address these problems, we propose an adaptive LiDAR attack recognition framework capable of adjusting to different driving scenarios. This framework initially models the perception system by integrating the vehicle dynamics model and object tracking algorithms to extract data features, subsequently employing Gaussian Processes for the probabilistic modeling of these features. Finally, the framework employs sparsification computing techniques and a sliding window strategy to continuously update the Gaussian Process model with window data, which achieves incremental learning that generates uncertainty estimates as dynamic anomaly boundaries to recognize attacks. The performance of the proposed framework has been evaluated extensively using the real-world KITTI dataset covering four driving scenarios. Compared to previous methods, our framework achieves a 100% accuracy rate and a 0% false positive rate in the localization system, and an average increase of 3.43% in detection accuracy in the detection system across the four scenarios, which demonstrates superior adaptive capabilities. [ABSTRACT FROM AUTHOR]

Recently, using Bayesian Machine Learning, a deviation from the cold dark matter model on cosmological scales has been put forward. Such a model might replace the proposed non-gravitational interaction between dark energy and dark matter, and help solve the H 0 tension problem. The idea behind the learning procedure relies on a generated expansion rate, while the real expansion rate is just used to validate the learned results. In the present work, however, the emphasis is put on a Gaussian Process (GP), with the available H (z) data confirming the possible existence of the already learned deviation. Three cosmological scenarios are considered: a simple one, with an equation-of-state parameter for dark matter ω d m = ω 0 ≠ 0 , and two other models, with corresponding parameters ω d m = ω 0 + ω 1 z and ω d m = ω 0 + ω 1 z / (1 + z) . The constraints obtained on the free parameters ω 0 and ω 1 hint towards a dynamical nature of the deviation. The dark energy dynamics is also reconstructed, revealing interesting aspects connected with the H 0 tension problem. It is concluded, however, that improved tools and more data are needed, to reach a better understanding of the reported deviation. [ABSTRACT FROM AUTHOR]

The analysis and research of composite structure specimens depend on test methods. However, due to the high cost, complex test conditions, time-consuming, and other problems, it is difficult to carry out a large number of tests. A large amount of data is often required for parametric analysis and structural optimization of composite structure specimens. Therefore, to solve the problem of insufficient data samples in the analysis and research of specimens. In this paper, a finite element model updating method based on Bayesian theory and a Gaussian process data fusion method is proposed, that is, the amount of data is expanded by the proposed model updating method, and then the experimental and numerical simulation data are fused based on the Gaussian process data fusion method. Finally, the effectiveness of the proposed model updating method and data fusion method is verified by a numerical example of π type beam-column joints. The results show that the method has high generalization ability and prediction accuracy in the case of small samples through the fusion of numerical simulation and experimental data. [ABSTRACT FROM AUTHOR]

We use Brascamp-Lieb's inequality to obtain new decoupling inequalities for general Gaussian vectors, and in particular for finite stationary Gaussian processes. In the second case, we provide an application using a version by Bump and Diaconis of the strong Szegö limit theorem. We obtain sharp estimates on the decoupling coefficient of remarkable classes of Gaussian processes. [ABSTRACT FROM AUTHOR]

In this paper, we provide a unified approach to simulate diffusion bridges. The proposed method covers a wide range of processes including univariate and multivariate diffusions, and the diffusions can be either time-homogeneous or time-inhomogeneous. We provide a theoretical framework for the proposed method. In particular, using the parametrix representations we show that the approximated probability transition density function converges to that of the true diffusion, which in turn implies the convergence of the approximation. Unlike most of the methods proposed in the literature, our approach does not involve acceptance-rejection mechanics. That is, it is acceptance-rejection free. Extensive numerical examples are provided for illustration and demonstrate the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

This study proposes an approach of leveraging information gathered from multiple traffic data sources at different resolutions to obtain approximate inference on the traffic distribution of Chicago's O'Hare Airport area. Specifically, it proposes the ingestion of traffic datasets at different resolutions to build spatiotemporal models for predicting the distribution of traffic volume on the road network. Due to its good adaptability and flexibility for spatiotemporal data, the Gaussian process (GP) regression was employed to provide short-term forecasts using data collected by loop detectors (sensors) and supplemented by telematics data. The GP regression is used to make predictions of the distribution of the proportion of sensor data traffic volume represented by the telematics data for each location of the sensors. Consequently, the fitted GP model can be used to determine the approximate traffic distribution for a testing location outside of the training points. Policymakers in the transportation sector can find the results of this work helpful for making informed decisions relating to current and future transportation conditions in the area. [ABSTRACT FROM AUTHOR]

ABSTRACT The determination of flash points is a critical aspect of chemical safety, essential for assessing explosion hazards and fire risks associated with flammable solutions. With the advent of new chemical blends and the increasing complexity of chemical waste management, the need for accurate and reliable flash point prediction methods has become more pronounced. This study introduces a novel predictive approach using Bayesian kernel machine regression (BKMR) with Gaussian process priors, designed to meet the growing demand for precise flash point estimation in the context of chemical safety. The BKMR model, underpinned by Bayesian statistics, offers a comprehensive framework that not only quantifies prediction uncertainty but also enhances interpretability amidst experimental data variability. Our comparative analysis reveals that BKMR surpasses traditional predictive models, including support vector machines, kernel ridge regression, and Gaussian process regression, in terms of accuracy and reliability across multiple metrics. By elucidating the intricate interactions between molecular features and flash point properties, the BKMR model provides profound insights into the chemical dynamics that influence flash point determinations. This study signifies a methodological leap in flash point prediction, offering a valuable tool for chemical safety analysis and contributing to the development of safer chemical handling and storage practices. [ABSTRACT FROM AUTHOR]

This paper presents a non-parametric Bayesian approach for modeling multiple response variables using a Gaussian process regression (GPR) model. The response functions are modeled using a dependent Gaussian process (GP) prior, and the estimation, prediction, and inference issues are discussed within this framework. To establish the information consistency of the dependent GPs prediction strategy, a stretching-restriction method is proposed. The covariance structure is constructed using convolved Gaussian processes (CGPs) to illustrate the results. Simulations and real data analyses show that the proposed dependent GPR yields reasonably good prediction accuracy. [ABSTRACT FROM AUTHOR]

This article is concerned with sample size determination methodology for prediction models. We propose to combine the individual calculations via learning‐type curves. We suggest two distinct ways of doing so, a deterministic skeleton of a learning curve and a Gaussian process centered upon its deterministic counterpart. We employ several learning algorithms for modeling the primary endpoint and distinct measures for trial efficacy. We find that the performance may vary with the sample size, but borrowing information across sample size universally improves the performance of such calculations. The Gaussian process‐based learning curve appears more robust and statistically efficient, while computational efficiency is comparable. We suggest that anchoring against historical evidence when extrapolating sample sizes should be adopted when such data are available. The methods are illustrated on binary and survival endpoints. [ABSTRACT FROM AUTHOR]

In this article, we develop an analytical approach for estimating brain connectivity networks that accounts for subject heterogeneity. More specifically, we consider a novel extension of a multi‐subject Bayesian vector autoregressive model that estimates group‐specific directed brain connectivity networks and accounts for the effects of covariates on the network edges. We adopt a flexible approach, allowing for (possibly) nonlinear effects of the covariates on edge strength via a novel Bayesian nonparametric prior that employs a weighted mixture of Gaussian processes. For posterior inference, we achieve computational scalability by implementing a variational Bayes scheme. Our approach enables simultaneous estimation of group‐specific networks and selection of relevant covariate effects. We show improved performance over competing two‐stage approaches on simulated data. We apply our method on resting‐state functional magnetic resonance imaging data from children with a history of traumatic brain injury (TBI) and healthy controls to estimate the effects of age and sex on the group‐level connectivities. Our results highlight differences in the distribution of parent nodes. They also suggest alteration in the relation of age, with peak edge strength in children with TBI, and differences in effective connectivity strength between males and females. [ABSTRACT FROM AUTHOR]

AbstractApproximate Bayesian computation (ABC) is a class of Bayesian inference algorithms that targets problems with intractable or unavailable likelihood functions. It uses synthetic data drawn from the simulation model to approximate the posterior distribution. However, ABC is computationally intensive for complex models in which simulating synthetic data is very expensive. In this article, we propose an early rejection Markov chain Monte Carlo (ejMCMC) sampler based on Gaussian processes to accelerate inference speed. We early reject samples in the first stage of the kernel using a discrepancy model, in which the discrepancy between the simulated and observed data is modeled by Gaussian process (GP). Hence, synthetic data is generated only if the parameter space is worth exploring. We demonstrate through theory, simulation experiments, and real data analysis that the new algorithm significantly improves inference efficiency compared to existing early-rejection MCMC algorithms. In addition, we employ our proposed method within an ABC sequential Monte Carlo (SMC) sampler. In our numerical experiments, we use examples of ordinary differential equations, stochastic differential equations, and delay differential equations to demonstrate the effectiveness of the proposed algorithm. We develop an R package that is available at https://github.com/caofff/ejMCMC. [ABSTRACT FROM AUTHOR]

Accurate streamflow forecasting is crucial for effectively managing water resources, particularly in countries like Colombia, where hydroelectric power generation significantly contributes to the national energy grid. Although highly interpretable, traditional deterministic, physically-driven models often suffer from complexity and require extensive parameterization. Data-driven models like Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) networks offer simplicity and performance but cannot quantify uncertainty. This work introduces Sparse Variational Gaussian Processes (SVGPs) for forecasting streamflow contributions. The proposed SVGP model reduces computational complexity compared to traditional Gaussian Processes, making it highly scalable for large datasets. The methodology employs optimal hyperparameters and shared inducing points to capture short-term and long-term relationships among reservoirs. Training, validation, and analysis of the proposed approach consider the streamflow dataset from 23 geographically dispersed reservoirs recorded during twelve years in Colombia. Performance assessment reveals that the proposal outperforms baseline Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) models in three key aspects: adaptability to changing dynamics, provision of informative confidence intervals through Bayesian inference, and enhanced forecasting accuracy. Therefore, the SVGP-based forecasting methodology offers a scalable and interpretable solution for multi-output streamflow forecasting, thereby contributing to more effective water resource management and hydroelectric planning. [ABSTRACT FROM AUTHOR]

AbstractComputer simulations have become essential for analyzing complex systems, but high-fidelity simulations often come with significant computational costs. To tackle this challenge, multi-fidelity computer experiments have emerged as a promising approach that leverages both low-fidelity and high-fidelity simulations, enhancing both the accuracy and efficiency of the analysis. In this article, we introduce a new and flexible statistical model, the Recursive Non-Additive (RNA) emulator, that integrates the data from multi-fidelity computer experiments. Unlike conventional multi-fidelity emulation approaches that rely on an additive auto-regressive structure, the proposed RNA emulator recursively captures the relationships between multi-fidelity data using Gaussian process priors without making the additive assumption, allowing the model to accommodate more complex data patterns. Importantly, we derive the posterior predictive mean and variance of the emulator, which can be efficiently computed in a closed-form manner, leading to significant improvements in computational efficiency. Additionally, based on this emulator, we introduce four active learning strategies that optimize the balance between accuracy and simulation costs to guide the selection of the fidelity level and input locations for the next simulation run. We demonstrate the effectiveness of the proposed approach in a suite of synthetic examples and a real-world problem. An R package RNAmf for the proposed methodology is provided on CRAN. [ABSTRACT FROM AUTHOR]

Geomagnetic field models over past millennia rely on two main data sources: archeomagnetic data provide snapshots of the geomagnetic field at specific locations, and sediment records deliver time series of the geomagnetic field at specific locations. The limited temporal and spatial coverage of archeomagnetic data necessitates the incorporation of sediment data especially when models go further back in time. When working with sediment data one should consider the post‐depositional detrital remanent magnetization (pDRM) process, which can cause delayed and smoothed signals. To address the distortion associated with the pDRM process a Bayesian modeling technique incorporating archeomagnetic data and a class of flexible parameterized lock‐in functions has been proposed. In this study, we investigate this method in more detail and apply it to declination and inclination of several lacustrine and marine sediment records. Data‐driven results support the hypothesis that the pDRM process can introduce distortions, including offsets and smoothing, in some lacustrine and marine sediment records. We demonstrate a correction approach to minimize the distortion caused by the pDRM process and its impact on geomagnetic field reconstructions. The variability in the results observed across the nine records points to a potential dependence on sedimentological characteristics. To explore this further, we plan to systematically apply our novel method to a larger number of records in future studies. Plain Language Summary: Understanding the Earth's magnetic field changes over the past millennia helps us learn more about the planet's history. We can use the magnetic field information preserved in different materials to reconstruct the past Earth's magnetic field evolution: ancient artifacts (archeomagnetic data), lava flows and sediment records. Archeomagnetic and lava flow data has limited coverage in time and space, so when modeling longer time scales we have to rely more and more on sediment data. When using sediment data, we need to be careful about a process called post‐depositional detrital remanent magnetization (pDRM), which can distort the signals and cause smoothing and delays. To deal with this issue, a new method has been developed using Bayesian modeling, archeomagnetic data and flexible lock‐in functions to correct for the pDRM effect. In this study we explore this method in more detail and test it on several lacustrine and marine sediment records. We found that the pDRM process indeed introduces distortions in several sediment records. Key Points: We estimate homogenous lock‐in functions for several lacustrine and marine sediment recordsWe propose a new method to transform relative declinations to absolute valuesThe large variety of estimated lock‐in functions indicates the importance of taking post‐depositional detrital remanent magnetization distortions into account [ABSTRACT FROM AUTHOR]

In many applications that involve the inference of an unknown smooth function, the inference of its derivatives is also important. To make joint inferences of the function and its derivatives, a class of Gaussian processes called pth order Integrated Wiener's Process (IWP), is considered. Methods for constructing a finite element (FEM) approximation of an IWP exist but only focus on the case p = 2 and do not allow appropriate inference for derivatives. In this article, we propose an alternative FEM approximation with overlapping splines (O-spline). The O-spline approximation applies for any order p ∈ Z + , and provides consistent and efficient inference for all derivatives up to order p – 1. It is shown both theoretically and empirically that the O-spline approximation converges to the IWP as the number of knots increases. We further provide a unified and interpretable way to define priors for the smoothing parameter based on the notion of predictive standard deviation, which is invariant to the order p and the knot placement. Finally, we demonstrate the practical use of the O-spline approximation through an analysis of COVID death rates where the inference of derivative has an important interpretation in terms of the course of the pandemic. for this article are available online. [ABSTRACT FROM AUTHOR]

Max-stable processes are the most popular models for high-impact spatial extreme events, as they arise as the only possible limits of spatially-indexed block maxima. However, likelihood inference for such models suffers severely from the curse of dimensionality, since the likelihood function involves a combinatorially exploding number of terms. In this article, we propose using the Vecchia approximation, which conveniently decomposes the full joint density into a linear number of low-dimensional conditional density terms based on well-chosen conditioning sets designed to improve and accelerate inference in high dimensions. Theoretical asymptotic relative efficiencies in the Gaussian setting and simulation experiments in the max-stable setting show significant efficiency gains and computational savings using the Vecchia likelihood approximation method compared to traditional composite likelihoods. Our application to extreme sea surface temperature data at more than a thousand sites across the entire Red Sea further demonstrates the superiority of the Vecchia likelihood approximation for fitting complex models with intractable likelihoods, delivering significantly better results than traditional composite likelihoods, and accurately capturing the extremal dependence structure at lower computational cost. for this article are available online. [ABSTRACT FROM AUTHOR]

This paper presents a physics-free Bayesian approach for the learning and inference of probabilistic stability charts in milling operations. The approach does not require any information from machine tool structural dynamics or cutting force coefficients, and the underlying learning algorithm can operate with limited training data. A Fully Bayesian Gaussian Process with distributions on its kernel hyperparameters is employed to enable information transfer between different machine and process configurations. The vision system further automates the detection of necessary dimensions from the tool–holder assembly in the machine's tool magazine, further enhancing the applicability of the approach. Experiments demonstrated the effectiveness of this approach, offering great promise as an industry-friendly solution. [ABSTRACT FROM AUTHOR]

Admixture between populations and species is common in nature. Since the influx of new genetic material might be either facilitated or hindered by selection, variation in mixture proportions along the genome is expected in organisms undergoing recombination. Various graph-based models have been developed to better understand these evolutionary dynamics of population splits and mixtures. However, current models assume a single mixture rate for the entire genome and do not explicitly account for linkage. Here, we introduce TreeSwirl , a novel method for inferring branch lengths and locus-specific mixture proportions by using genome-wide allele frequency data, assuming that the admixture graph is known or has been inferred. TreeSwirl builds upon TreeMix that uses Gaussian processes to estimate the presence of gene flow between diverged populations. However, in contrast to TreeMix , our model infers locus-specific mixture proportions employing a hidden Markov model that accounts for linkage. Through simulated data, we demonstrate that TreeSwirl can accurately estimate locus-specific mixture proportions and handle complex demographic scenarios. It also outperforms related D - and f -statistics in terms of accuracy and sensitivity to detect introgressed loci. [ABSTRACT FROM AUTHOR]

Fluorescence lifetime imaging microscopy (FLIM) has become a standard tool in the quantitative characterization of subcellular environments. However, quantitative FLIM analyses face several challenges. First, spatial correlations between pixels are often ignored as signal from individual pixels is analyzed independently thereby limiting spatial resolution. Second, existing methods deduce photon ratios instead of absolute lifetime maps. Next, the number of fluorophore species contributing to the signal is unknown, while excited state lifetimes with

Variable-density groundwater flow (VDGF) is jointly driven by hydraulic and density gradient, leading to strong nonlinearity, large computational burden of numerical models, and therefore huge computational cost of Monte Carlo simulation for uncertainty analysis. This study developed the reduced-order model (ROM) for VDGF and built the Gaussian process (GP) for simulating the numerical error of the ROM. The coupled model can obtain solutions of head and salinity across the study domain while GP simulates observation information at limited locations. Moreover, the coupled model can provide higher solution accuracies of head and salinity at the observation locations than the ROM. A two-dimensional (cross-section) VDGF test case was considered, where hydraulic conductivity was taken as a spatially random field. MC simulations were performed using three models, including the full-system model, the ROM, and the coupled model, with corresponding MC strategies denoted as FSMC, ROMC, and GP-ROMC, respectively. The results show that ROMC can be an alternative to FSMC for conducting uncertainty quantification. The relationship between head (or salinity) and the dimensional of ROM can be characterized using power functions with determinate coefficients larger than 0.99. GP-ROMC has higher solution accuracy than ROMC, which indicates that GP is capable for simulating the numerical error of ROM. The results in this study are significant for performing simulation, uncertainty quantification, risk assessment, and parameter estimate in the context of groundwater.

Information on the physicochemical properties of chemical species is an important prerequisite when performing tasks such as process design and product design. However, the lack of extensive data and high experimental costs hinder the development of prediction techniques for these properties. Moreover, accuracy and predictive capabilities still limit the scope and applicability of most property estimation methods. This paper proposes a new Gaussian process-based modeling framework that aims to manage a discrete and high-dimensional input space related to molecular structure representation with the group-contribution approach. A warping function is used to map discrete input into a continuous domain in order to adjust the correlation between different compounds. Prior selection techniques, including prior elicitation and prior predictive checking, are also applied during the building procedure to provide the model with more information from previous research findings. The framework is assessed using datasets of varying sizes for 20 pure component properties. For 18 out of the 20 pure component properties, the new models are found to give improved accuracy and predictive power in comparison with other published models, with and without machine learning.

This study proposes an approach of leveraging information gathered from multiple traffic data sources at different resolutions to obtain approximate inference on the traffic distribution of Chicago's O'Hare Airport area. Specifically, it proposes the ingestion of traffic datasets at different resolutions to build spatiotemporal models for predicting the distribution of traffic volume on the road network. Due to its good adaptability and flexibility for spatiotemporal data, the Gaussian process (GP) regression was employed to provide short-term forecasts using data collected by loop detectors (sensors) and supplemented by telematics data. The GP regression is used to make predictions of the distribution of the proportion of sensor data traffic volume represented by the telematics data for each location of the sensors. Consequently, the fitted GP model can be used to determine the approximate traffic distribution for a testing location outside of the training points. Policymakers in the transportation sector can find the results of this work helpful for making informed decisions relating to current and future transportation conditions in the area.

In this study, we show that pollutants of emerging concern are, by nature, prone to the emergence of epistemic uncertainty. We also show that the current uncertainty quantification methods used for pollutant modelling rely almost exclusively on parameter uncertainty, which is not adequate to tackle epistemic uncertainty affecting the model structure. We, therefore, suggest a paradigm shift in the current pollutant modelling approaches by adding a term explicitly accounting for epistemic uncertainties. In a proof-of-concept, we use this approach to investigate the impact of epistemic uncertainty in the fluctuation of pollutants during wet-weather discharge (input information) on the distribution of mass of pollutants (output distributions). We found that the range of variability negatively impacts the tail of output distributions. The fluctuation time, associated with high covariance between discharge and concentration, is a major driver for the output distributions. Adapting to different levels of epistemic uncertainty, our approach helps to identify critical unknown information in the fluctuation of pollutant concentration. Such information can be used in a risk management context and to design smart monitoring campaigns. HIGHLIGHTS Current modelling approaches are not suitable for the deep epistemic uncertainty associated with pollutants of emerging concern.; Variability and fluctuation of concentration and the concentration-discharge dependency can worsen the severity of an overflow event.; Through our method for the impact of epistemic uncertainty, we suggest a paradigm shift toward the design of smart stormwater quality monitoring campaigns.;

Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at different parameter settings. Using intelligent and adaptive selection of parameters to build the emulator can drastically improve the efficiency of the calibration process. The article proposes a sequential framework with a novel criterion for parameter selection that targets learning the posterior density of the parameters. The emergent behavior from this criterion is that exploration happens by selecting parameters in uncertain posterior regions while simultaneously exploitation happens by selecting parameters in regions of high posterior density. The advantages of the proposed method are illustrated using several simulation experiments and a nuclear physics reaction model.