We seek to understand the factors that drive mortality in the contiguous United States using data that are indexed by county and year and grouped into 18 different age bins. We propose a model that adds two important contributions to existing mortality studies. First, we treat age as a random effect. This is an improvement over previous models because it allows the model in one age group to borrow information from other age groups. Second, we utilize Gaussian Processes to create nonlinear covariate effects for predictors such as unemployment rate, race, and education level. This allows for a more flexible relationship to be modeled between mortality and these predictors. Understanding that the United States is expansive and diverse, we allow for many of these effects to vary by location. The flexibility in how predictors relate to mortality has not been used in previous mortality studies and will result in a more accurate model and a more complete understanding of the factors that drive mortality. Both the multivariate nature of the model as well as the spatially varying non-linear predictors will advance the study of mortality and will allow us to better examine the relationships between the predictors and mortality.

Reduction in mobility due to gait impairment is a critical consequence of diseases affecting the neuromusculoskeletal system, making detecting anomalies in a person’s gait a key area of interest. This challenge is compounded by within-subject and between-subject variability, further emphasized in individuals with multiple sclerosis (MS), where gait patterns exhibit significant heterogeneity. This study introduces a novel perspective on modeling kinematic gait patterns, recognizing the inherent hierarchical structure of the data, which is gathered from contralateral limbs, individuals, and groups of individuals comprising a population, using wearable sensors. Rather than summarizing features, this approach models the entire gait cycle functionally, including its variation. A Hierarchical Variational Sparse Heteroscedastic Gaussian Process was used to model the shank angular velocity across 28 MS and 28 healthy individuals. The utility of this methodology was underscored by its granular analysis capabilities. This facilitated a range of quantifiable comparisons, spanning from group-level assessments to patient-specific analyses, addressing the complexity of pathological gait patterns and offering a robust methodology for kinematic pattern characterization for large datasets. The group-level analysis highlighted notable differences during the swing phase and towards the end of the stance phase, aligning with previously established literature findings. Moreover, the study identified the heteroscedastic gait pattern variability as a distinguishing feature of MS gait. Additionally, a novel approach for lower limb gait asymmetry quantification has been proposed. The use of probabilistic hierarchical modeling facilitated a better understanding of the impaired gait pattern, while also expressing potential for extrapolation to other pathological conditions affecting gait.

The continuous random energy model (CREM) was introduced by Bovier and Kurkova in 2004 as a toy model of disordered systems. Among other things, their work indicates that there exists a critical point $\beta_\mathrm{c}$ such that the partition function exhibits a phase transition. The present work focuses on the high-temperature regime where $\beta<\beta_\mathrm{c}$. We show that, for all $\beta<\beta_\mathrm{c}$ and for all $s>0$, the negative s moment of the CREM partition function is comparable with the expectation of the CREM partition function to the power of $-s$, up to constants that are independent of N.

This paper presents an efficient trajectory planning method for a 4-DOF robotic arm designed for pick-and-place manipulation tasks. The method addresses several challenges, where traditional optimization approaches struggle with high dimensionality, and data-driven methods are costly to collect enough data. The proposed approach leverages Bézier curves for computationally efficient, smooth trajectory generation, minimizing abrupt changes in motion. When continuous solutions for the end-effector angle are unavailable, joint angles are interpolated using Bézier or Hermite interpolation. Additionally, we use custom metrics to evaluate deviation between the interpolated trajectory and the original trajectory, as well as the overall smoothness of the path. When a continuous solution exists, the trajectory is treated as a Gaussian process, where a prior factor is generated using the centerline. This prior is then combined with a smoothness factor to optimize the trajectory, ensuring it remains as smooth as possible within the feasible solution space through stochastic gradient descent. The method is evaluated through simulations in Nvidia Isaac Sim; results highlight the method’s suitability, and future work will explore enhancements in prior trajectory integration and smoothing techniques.

Mobile robots are a key component for the automation of many tasks that either require high precision or are deemed too hazardous for human personnel. One of the typical duties for mobile robots in the industrial sector is to perform trajectory tracking, which involves pursuing a specific path through both space and time. In this paper, an iterative learning-based procedure for highly accurate tracking is proposed. This contribution shows how data-based techniques, namely Gaussian process regression, can be used to tailor a motion model to a specific reoccurring reference. The procedure is capable of explorative behavior meaning that the robot automatically explores states around the prescribed trajectory, enriching the data set for learning and increasing the robustness and practical training accuracy. The trade-off between highly accurate tracking and exploration is done automatically by an optimization-based reference generator using a suitable cost function minimizing the posterior variance of the underlying Gaussian process model. While this study focuses on omnidirectional mobile robots, the scheme can be applied to a wide range of mobile robots. The effectiveness of this approach is validated in meaningful real-world experiments on a custom-built omnidirectional mobile robot where it is shown that explorative behavior can outperform purely exploitative approaches.

Simulations of future climate contain variability arising from a number of sources, including internal stochasticity and external forcings. However, to the best of our abilities climate models and the true observed climate depend on the same underlying physical processes. In this paper, we simultaneously study the outputs of multiple climate simulation models and observed data, and we seek to leverage their mean structure as well as interdependencies that may reflect the climate’s response to shared forcings. Bayesian modeling provides a fruitful ground for the nuanced combination of multiple climate simulations. We introduce one such approach whereby a Gaussian process is used to represent a mean function common to all simulated and observed climates. Dependent random effects encode possible information contained within and between the plurality of climate model outputs and observed climate data. We propose an empirical Bayes approach to analyze such models in a computationally efficient way. This methodology is amenable to the CMIP6 model ensemble, and we demonstrate its efficacy at forecasting global average near-surface air temperature. Results suggest that this model and the extensions it engenders may provide value to climate prediction and uncertainty quantification.

Wind turbine towers are subjected to highly varying internal loads, characterized by large uncertainty. The uncertainty stems from many factors, including what the actual wind fields experienced over time will be, modeling uncertainties given the various operational states of the turbine with and without controller interaction, the influence of aerodynamic damping, and so forth. To monitor the true experienced loading and assess the fatigue, strain sensors can be installed at fatigue-critical locations on the turbine structure. A more cost-effective and practical solution is to predict the strain response of the structure based only on a number of acceleration measurements. In this contribution, an approach is followed where the dynamic strains in an existing onshore wind turbine tower are predicted using a Gaussian process latent force model. By employing this model, both the applied dynamic loading and strain response are estimated based on the acceleration data. The predicted dynamic strains are validated using strain gauges installed near the bottom of the tower. Fatigue is subsequently assessed by comparing the damage equivalent loads calculated with the predicted as opposed to the measured strains. The results confirm the usefulness of the method for continuous tracking of fatigue life consumption in onshore wind turbine towers.

Tree-ring chronologies encode interannual variability in forest growth rates over long time periods from decades to centuries or even millennia. However, each chronology is a highly localized measurement describing conditions at specific sites where wood samples have been collected. The question whether these local growth variabilites are representative for large geographical regions remains an open issue. To overcome the limitations of interpreting a sparse network of sites, we propose an upscaling approach for annual tree-ring indices that approximate forest growth variability and compute gridded data products that generalize the available information for multiple tree genera. Using regression approaches from machine learning, we predict tree-ring indices in space and time based on climate variables, but considering also species range maps as constraints for the upscaling. We compare various prediction strategies in cross-validation experiments to identify the best performing setup. Our estimated maps of tree-ring indices are the first data products that provide a dense view on forest growth variability at the continental level with 0.5° and 0.0083° spatial resolution covering the years 1902–2013. Furthermore, we find that different genera show very variable spatial patterns of anomalies. We have selected Europe as study region and focused on the six most prominent tree genera, but our approach is very generic and can easily be applied elsewhere. Overall, the study shows perspectives but also limitations for reconstructing spatiotemporal dynamics of complex biological processes. The data products are available at https://www.doi.org/10.17871/BACI.248.

Reduced-order models (ROMs) are computationally inexpensive simplifications of high-fidelity complex ones. Such models can be found in computational fluid dynamics where they can be used to predict the characteristics of multiphase flows. In previous work, we presented a ROM analysis framework that coupled compression techniques, such as autoencoders, with Gaussian process regression in the latent space. This pairing has significant advantages over the standard encoding–decoding routine, such as the ability to interpolate or extrapolate in the initial conditions’ space, which can provide predictions even when simulation data are not available. In this work, we focus on this major advantage and show its effectiveness by performing the pipeline on three multiphase flow applications. We also extend the methodology by using deep Gaussian processes as the interpolation algorithm and compare the performance of our two variations, as well as another variation from the literature that uses long short-term memory networks, for the interpolation.

Electromagnetic simulation software has become an important tool for antenna design. However, high-fidelity simulation of wideband or ultra-wideband antennas is very expensive. Therefore, antenna optimization design by using an electromagnetic solver may be limited due to its high computational cost. This problem can be alleviated by the utilization of fast and accurate surrogate models. Unfortunately, conventional surrogate models for antenna design are usually prohibitive because training data acquisition is time-consuming. In order to solve the problem, a modeling method named progressive Gaussian process (PGP) is proposed in this study. Specially, when a Gaussian process (GP) is trained, test sample with the largest predictive variance is inputted into an electromagnetic solver to simulate its results. After that, the test sample is added to the training set to train the GP progressively. The process can incrementally increase some important trusted training data and improve the model generalization performance. Based on the proposed PGP, two monopole antennas are optimized. The optimization results show effectiveness and efficiency of the method.

This paper studies the joint tail asymptotics of extrema of the multi-dimensional Gaussian process over random intervals defined as $P(u)\;:\!=\; \mathbb{P}\{\cap_{i=1}^n (\sup_{t\in[0,\mathcal{T}_i]} ( X_{i}(t) +c_i t )>a_i u )\}$, $u\rightarrow\infty$, where $X_i(t)$, $t\ge0$, $i=1,2,\ldots,n$, are independent centered Gaussian processes with stationary increments, $\boldsymbol{\mathcal{T}}=(\mathcal{T}_1, \ldots, \mathcal{T}_n)$ is a regularly varying random vector with positive components, which is independent of the Gaussian processes, and $c_i\in \mathbb{R}$, $a_i>0$, $i=1,2,\ldots,n$. Our result shows that the structure of the asymptotics of P(u) is determined by the signs of the drifts $c_i$. We also discuss a relevant multi-dimensional regenerative model and derive the corresponding ruin probability.

We present a hierarchical Dirichlet regression model with Gaussian process priors that enables accurate and well-calibrated forecasts for U.S. Senate elections at varying time horizons. This Bayesian model provides a balance between predictions based on time-dependent opinion polls and those made based on fundamentals. It also provides uncertainty estimates that arise naturally from historical data on elections and polls. Experiments show that our model is highly accurate and has a well calibrated coverage rate for vote share predictions at various forecasting horizons. We validate the model with a retrospective forecast of the 2018 cycle as well as a true out-of-sample forecast for 2020. We show that our approach achieves state-of-the art accuracy and coverage despite relying on few covariates.

We study, under mild conditions, the weak approximation constructed from a standard Poisson process for a class of Gaussian processes, and establish its sample path moderate deviations. The techniques consist of a good asymptotic exponential approximation in moderate deviations, the Besov–Lèvy modulus embedding, and an exponential martingale technique. Moreover, our results are applied to the weak approximations associated with the moving average of Brownian motion, fractional Brownian motion, and an Ornstein–Uhlenbeck process.

We investigate joint modelling of longevity trends using the spatial statistical framework of Gaussian process (GP) regression. Our analysis is motivated by the Human Mortality Database (HMD) that provides unified raw mortality tables for nearly 40 countries. Yet few stochastic models exist for handling more than two populations at a time. To bridge this gap, we leverage a spatial covariance framework from machine learning that treats populations as distinct levels of a factor covariate, explicitly capturing the cross-population dependence. The proposed multi-output GP models straightforwardly scale up to a dozen populations and moreover intrinsically generate coherent joint longevity scenarios. In our numerous case studies, we investigate predictive gains from aggregating mortality experience across nations and genders, including by borrowing the most recently available “foreign” data. We show that in our approach, information fusion leads to more precise (and statistically more credible) forecasts. We implement our models in R, as well as a Bayesian version in Stan that provides further uncertainty quantification regarding the estimated mortality covariance structure. All examples utilise public HMD datasets.