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This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate…

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…

Big Data often presents as massive non-probability samples. Not only is the selection mechanism often unknown, but larger data volume amplifies the relative contribution of selection bias to total error. Existing bias adjustment approaches…

In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

We present a methodology for quantifying seismic velocity and pore pressure uncertainty that incorporates information regarding the geological history of a basin, rock physics, well log, drilling and seismic data. In particular, our…

Whenever oceanic currents flow over rough topography, there is an associated stress that acts to modify the flow. In the deep ocean, this stress is predominantly a form drag due to pressure differentials across topography, caused by the…

A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of…

Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to…

Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…

This study presents a novel approach to quantifying uncertainties in Bayesian model updating, which is effective in sparse or single observations. Conventional uncertainty quantification metrics such as the Euclidean and Bhattacharyya…

Analysis of observational studies increasingly confronts the challenge of determining which of a possibly high-dimensional set of available covariates are required to satisfy the assumption of ignorable treatment assignment for estimation…

With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial…

This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…

Physics-based covariance models provide a systematic way to construct covariance models that are consistent with the underlying physical laws in Gaussian process analysis. The unknown parameters in the covariance models can be estimated…

Geological process models simulate a range of dynamic processes to evolve a base topography into a final 2D cross-section or 3D geological scenario. In principle, process parameters may be updated to better align with observed geophysical…

Adapting pre-trained deep learning models to new and unknown environments remains a major challenge in underwater acoustic localization. We show that although the performance of pre-trained models suffers from mismatch between the training…