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Nonlinear relationships between covariates and a response variable of interest are frequently encountered in animal science research. Within statistical models, these nonlinear effects have, traditionally, been handled using a range of…
We introduce a framework for updating large scale geospatial processes using a model-data synthesis method based on Bayesian hierarchical modelling. Two major challenges come from updating large-scale Gaussian process and modelling…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework…
Sparse Bayesian learning (SBL) has been extensively utilized in data-driven modeling to combat the issue of overfitting. While SBL excels in linear-in-parameter models, its direct applicability is limited in models where observations…
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…
A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
Statistical models often assume that data are generated near a structured, smooth, or low-dimensional set. A common approach is to use Bayesian latent variable models, in which each observation is associated with a latent coordinate on the…
This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined…
We propose a probabilistic extension of Wiener-Laguerre models for causal operator learning. Classical Wiener-Laguerre models parameterize stable linear dynamics using orthonormal Laguerre bases and apply a static nonlinear map to the…
In statistical research there usually exists a choice between structurally simpler or more complex models. We argue that, even if a more complex, locally stationary time series model were true, then a simple, stationary time series model…
In this paper, we present a new statistical approach to the problem of incorporating experimental observations into a mathematical model described by linear partial differential equations (PDEs) to improve the prediction of the state of a…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
Suppose a linear model y = Hx + n, where inputs x, n are independent Gaussian mixtures. The problem is to design the transfer matrix H so as to minimize the mean square error (MSE) when estimating x from y. This problem has important…
Leveraging nonlinear parametrizations for model reduction can overcome the Kolmogorov barrier that affects transport-dominated problems. In this work, we build on the reduced dynamics given by Neural Galerkin schemes and propose to…
Bayesian nonparametric marginal methods are very popular since they lead to fairly easy implementation due to the formal marginalization of the infinite-dimensional parameter of the model. However, the straightforwardness of these methods…
We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated $L_2$-distance without assuming the regression function space to be uniformly bounded. The framework is…