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In this paper we prove, under mild conditions, that the positive definiteness of the circulant matrix appearing in the circulant embedding method is always guaranteed, provided the enclosing cube is sufficiently large. We examine in detail…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
This paper is concerned with the study of the embedding circulant matrix method to simulate stationary complex-valued Gaussian sequences. The method is, in particular, shown to be well-suited to generate circularly-symmetric stationary…
We study random series priors for estimating a functional parameter (f\in L^2[0,1]). We show that with a series prior with random truncation, Gaussian coefficients, and inverse gamma multiplicative scaling, it is possible to achieve…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
We study the filtering and smoothing problem for continuous-time linear Gaussian systems. While classical approaches such as the Kalman-Bucy filter and the Rauch-Tung-Striebel (RTS) smoother provide recursive formulas for the conditional…
To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
We investigate the evolution of the phase-space distribution function around slightly perturbed stationary states and the process of violent relaxation in the context of the dissipationless collapse of an isolated spherical self-gravitating…
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…
Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, tapering can have poor performance when the process is sampled at spatially…
Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…
Characterizing time-periodic Hamiltonians is pivotal for validating and controlling driven quantum platforms, yet prevailing and unadjusted reconstruction methods demand dense time-domain sampling and heavy post-processing. We introduce a…
We present a new method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform…
We propose an approach to use the state covariance of linear systems to track time-varying covariance matrices of non-stationary time series. Following concepts from Riemmanian geometry, we investigate three types of covariance paths…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
The Mat\'ern covariance model is ubiquitous in spatial modelling, but there is no default choice for spatio-temporal modelling. In this paper, we consider the recently proposed ``diffusion-based'' extension of the spatial Mat\'ern…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…
This letter is concerned with solving continuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In the proposed smoothing method, we apply the TME method to approximate the transition density of the…