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Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…

We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression which provides a…

The majority of research on efficient and scalable algorithms in computational science and engineering has focused on the forward problem: given parameter inputs, solve the governing equations to determine output quantities of interest. In…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

Statistical early warning signs can be used to identify an approaching bifurcation in stochastic dynamical systems and are now regularly employed in applications concerned with the identification of potential rapid, non-linear change or…

Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior…

This is an introduction to Bayesian inference with a focus on hierarchical models and hyper-parameters. We write primarily for an audience of Bayesian novices, but we hope to provide useful insights for seasoned veterans as well. Examples…

Primordial features, in particular oscillatory signals, imprinted in the primordial power spectrum of density perturbations represent a clear window of opportunity for detecting new physics at high-energy scales. Future spectroscopic and…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

A typical audio signal processing pipeline includes multiple disjoint analysis stages, including calculation of a time-frequency representation followed by spectrogram-based feature analysis. We show how time-frequency analysis and…

Models that invoke nonlinear wavefront propagation in a chemically excitable medium are rife in the biological literature. Indeed, the idea that wavefront propagation can serve as a signaling mechanism has often been invoked to explain…

Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the…

As the number of gravitational-wave transient detections grows, the inclusion of marginally significant events in gravitational-wave catalogs will lead to increasing contamination from false positives. In this paper, we address the question…

We develop a spatio-temporal model to forecast sensor output at five locations in North East England. The signal is described using coupled dynamic linear models, with spatial effects specified by a Gaussian process. Data streams are…

The purpose of this study is to provide a new methodology of how one can consistently estimate a change-point in time series data. In contrast with previous studies, the suggested methodology employs only the empirical spectral density and…

Observational constraints on geomagnetic field changes from interannual to millenial periods are reviewed, and the current resolution of field models (covering archeological to satellite eras) is discussed. With the perspective of data…

Modeling of forests' vegetation in North Eurasia has been performed for 1982-2006 on the basis of remote sensing data. Four meteorological parameters and one parameter, characterizing geomagnetic field disturbance level, were used for this…

Earth observation from satellites offers the possibility to monitor our planet with unprecedented accuracy. Radiative transfer models (RTMs) encode the energy transfer through the atmosphere, and are used to model and understand the Earth…

The Neolithic Revolution began c. 10000 years ago and is characterised by the ultimate, near complete transition from hunting and gathering to agricultural food production on land. The Neolithic Revolution is thought to have been catalysed…

Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple…