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We consider the problem of estimating states and parameters in a model based on a system of coupled stochastic differential equations, based on noisy discrete-time data. Special attention is given to nonlinear dynamics and state-dependent…

This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are…

Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…

The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. A kernel-type estimators are used for estimation of the quadratic variation of the derivative of the limit of…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time.…

Differential privacy (DP) provides robust privacy guarantees for statistical inference, but this can lead to unreliable results and biases in downstream applications. While several noise-aware approaches have been proposed which integrate…

We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological…

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…

Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact…

Diffusive approximations of Markov jump processes often fail to accurately capture large fluctuations. This is confounding, as the rare events triggered by these large fluctuations, such as the failure of electronic memories, are often the…

Industrial processes generate a massive amount of monitoring data that can be exploited to uncover hidden time losses in the system. This can be used to enhance the accuracy of maintenance policies and increase the effectiveness of the…

This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive…

Hidden Markov models and their variants are the predominant sequential classification method in such domains as speech recognition, bioinformatics and natural language processing. Being generative rather than discriminative models, however,…

We consider a unified framework of sequential change-point detection and hypothesis testing modeled by means of hidden Markov chains. One observes a sequence of random variables whose distributions are functionals of a hidden Markov chain.…

We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…

Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a…

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…

We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…

Weak signal identification and inference are very important in the area of penalized model selection, yet they are under-developed and not well-studied. Existing inference procedures for penalized estimators are mainly focused on strong…