arXiv subjects

Claire Miller

Publications and source records attributed to Claire Miller.

7 recordsLinked to original sources

arXiv2026

A new framework for non-stationary spatio-temporal data fusion of multi-fidelity models

We propose a new scalable framework for spatio-temporal data fusion with multi-fidelity Gaussian processes (MFGPs) that enables fully likelihood-based inference for both stationary and non-stationary fidelity integration. The framework is designed for environmental applications, where abundant but noisy low-fidelity data (e.g., satellite or reanalysis products) must be fused with sparse yet accurate high-fidelity in-situ observations to obtain high-resolution reconstructions. Our key methodological contribution is a decomposed multi-fidelity covariance formulation that allows the Vecchia approximation to be applied directly to the latent low-fidelity and discrepancy processes. Combined with a Woodbury-based reconstruction, this yields a numerically stable and computationally efficient evaluation of the joint marginal likelihood without ever forming the full multi-fidelity covariance matrix. In addition, we introduce a generalized least squares (GLS) mean-removal strategy with fidelity-specific offsets, preventing systematic biases from being absorbed into cross-fidelity dependence. We validate the proposed approach through extensive experiments on synthetic data and a large-scale real-world application to wind speed reconstruction in the Lombardy region of Italy. The results show that the proposed Vecchia-based MFGP closely matches exact multi-fidelity inference in controlled settings, while substantially outperforming standard single-fidelity spatio-temporal Gaussian processes in terms of predictive accuracy, correlation, and representation of local variability in realistic large-data scenarios.

stat.CO↗

arXiv2025

A Bayesian INLA-SPDE Approach to Spatio-Temporal Point-Grid Fusion with Change-of-Support and Misaligned Covariates

We propose a spatio-temporal data-fusion framework for point data and gridded data with variables observed on different spatial supports. A latent Gaussian field with a Mat\'ern-SPDE prior provides a continuous space representation, while source-specific observation operators map observations to both point measurements and gridded averages, addressing change-of-support and covariate misalignment. Additionally incorporating temporal dependence enables prediction at unknown locations and time points. Inference and prediction are performed using the Integrated Nested Laplace Approximation and the Stochastic Partial Differential Equations approach, which delivers fast computation with uncertainty quantification. Our contributions are: a hierarchical model that jointly fuses multiple data sources of the same variable under different spatial and temporal resolutions and measurement errors, and a practical implementation that incorporates misaligned covariates via the same data fusion framework allowing differing covariate supports. We demonstrate the utility of this framework via simulations calibrated to realistic sensor densities and spatial coverage. Using the simulation framework, we explore the stability and performance of the approach with respect to the number of time points and data/covariate availability, demonstrating gains over single-source models through point and gridded data fusion. We apply our framework to soil moisture mapping in the Elliot Water catchment (Angus, Scotland). We fuse in-situ sensor data with aligned and misaligned covariates, satellite data and elevation data to produce daily high resolution maps with uncertainty.

stat.ME↗

arXiv2025

Network Weighted Functional Regression: a method for modeling dependencies between functional data in a network

In this paper, we propose a Network-Weighted Functional Regression (NWFR) model, an extension of Spatially Weighted Functional Regression (SWFR) to functional data defined on network-structured settings. To asses predictive uncertainity, we develop a functional conformal prediction procedure that yields a distribution free prediction intervals with guaranteed coverage. Through extensive evaluation on both simulated and real-world datasets, we demonstrate that the explicit modeling of network structure yields substantive improvements in point-prediction accuracy and markedly enhances the validity and precision of the resulting prediction intervals.

stat.ME↗

arXiv2024

Warped multifidelity Gaussian processes for data fusion of skewed environmental data

Understanding the dynamics of climate variables is paramount for numerous sectors, like energy and environmental monitoring. This study focuses on the critical need for a precise mapping of environmental variables for national or regional monitoring networks, a task notably challenging when dealing with skewed data. To address this issue, we propose a novel data fusion approach, the \textit{warped multifidelity Gaussian process} (WMFGP). The method performs prediction using multiple time-series, accommodating varying reliability and resolutions and effectively handling skewness. In an extended simulation experiment the benefits and the limitations of the methods are explored, while as a case study, we focused on the wind speed monitored by the network of ARPA Lombardia, one of the regional environmental agencies operting in Italy. ARPA grapples with data gaps, and due to the connection between wind speed and air quality, it struggles with an effective air quality management. We illustrate the efficacy of our approach in filling the wind speed data gaps through two extensive simulation experiments. The case study provides more informative wind speed predictions crucial for predicting air pollutant concentrations, enhancing network maintenance, and advancing understanding of relevant meteorological and climatic phenomena.

stat.AP↗

arXiv2023

Intrinsic Bayesian Optimisation on Complex Constrained Domain

Motivated by the success of Bayesian optimisation algorithms in the Euclidean space, we propose a novel approach to construct Intrinsic Bayesian optimisation (In-BO) on manifolds with a primary focus on complex constrained domains or irregular-shaped spaces arising as submanifolds of R2, R3 and beyond. Data may be collected in a spatial domain but restricted to a complex or intricately structured region corresponding to a geographic feature, such as lakes. Traditional Bayesian Optimisation (Tra-BO) defined with a Radial basis function (RBF) kernel cannot accommodate these complex constrained conditions. The In-BO uses the Sparse Intrinsic Gaussian Processes (SIn-GP) surrogate model to take into account the geometric structure of the manifold. SInGPs are constructed using the heat kernel of the manifold which is estimated as the transition density of the Brownian Motion on manifolds. The efficiency of In-BO is demonstrated through simulation studies on a U-shaped domain, a Bitten torus, and a real dataset from the Aral sea. Its performance is compared to that of traditional BO, which is defined in Euclidean space.

stat.ML↗

arXiv2022

Multiscale modelling of desquamation in the interfollicular epidermis

Maintenance of epidermal thickness is critical to the barrier function of the skin. Decreased tissue thickness, specifically in the stratum corneum (the outermost layer of the tissue), causes discomfort and inflammation, and is related to several severe diseases of the tissue. In order to maintain both stratum corneum thickness and overall tissue thickness it is necessary for the system to balance cell proliferation and cell loss. Cell proliferation in the epidermis occurs in the basal layer and causes constant upwards movement in the tissue. Cell loss occurs when dead cells at the top of the tissue are lost to the environment through a process called desquamation. Desquamation is thought to occur through a gradual reduction in adhesion between cells, due to the cleaving of adhesion proteins by enzymes, in the stratum corneum. In this paper we will investigate combining a (mass action) subcellular model of desquamation with a three dimensional (cell centre based) multicellular model of the interfollicular epidermis to better understand maintenance of epidermal thickness. These investigations show that hypothesised biological models for the degradation of cell-cell adhesion from the literature are able to provide a consistent rate of cell loss in the multicellular model. This loss balances proliferation, and hence maintains a homeostatic tissue thickness. Moreover, we find that multiple proliferative cell populations in the basal layer can be represented by a single proliferative cell population, simplifying investigations with this model. The model is used to investigate a disorder (Netherton Syndrome) which disrupts desquamation. The model shows how biochemical changes can cause disruptions to the tissue, resulting in a reduced tissue thickness and consequently diminishing the protective role of the tissue. A hypothetical treatment result is also investigated. [ABR]

q-bio.TO↗

arXiv2021

Maintaining the stem cell niche in multicellular models of epithelia

The maintenance of the proliferative cell niche is critical to epithelial tissue morphology and function. In this paper we investigate how current modelling methods can result in the erroneous loss of proliferative cells from the proliferative cell niche. Using an established model of the inter-follicular epidermis we find there is a limit to the proliferative cell densities that can be maintained in the basal layer (the niche) if we do not include additional mechanisms to stop the loss of proliferative cells from the niche. We suggest a new methodology that enables maintenance of a desired homeostatic population of proliferative cells in the niche: a rotational force is applied to the two daughter cells during the mitotic phase of division to enforce a particular division direction. We demonstrate that this new methodology achieves this goal. This methodology reflects the regulation of the orientation of cell division.

q-bio.TO↗