Related papers: Linear Stochastic Fluid Networks: Rare-Event Simul…
State-of-the-art methods for rare event simulation of non-Markovian models face practical or theoretical limits if observing the event of interest requires prior knowledge or information on the timed behavior of the system. In this paper,…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
This paper proposes niching importance sampling, a framework that combines concepts from reliability analysis, e.g. Markov chains, importance sampling, and relative cross entropy minimisation, with niching techniques from evolutionary…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…
We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process, computational cost can be prohibitive for networks of…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
Rare events are ubiquitous in many different fields, yet they are notoriously difficult to simulate because few, if any, events are observed in a conventiona l simulation run. Over the past several decades, specialised simulation methods…
Real-world (bio)chemical processes often exhibit stochastic dynamics with non-trivial correlations and state-dependent fluctuations. Model predictive control (MPC) often must consider these fluctuations to achieve reliable performance.…
We develop a predictive-first optimisation framework for streaming hidden Markov models. Unlike classical approaches that prioritise full posterior recovery under a fully specified generative model, we assume access to regime-specific…
We propose a unified framework for robustly and adaptively stabilizing large-scale networked uncertain Markovian jump linear systems (MJLS) under external disturbances and mode switches that can change the network's topology. Adaptation is…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
Optimal sensor scheduling with applications to networked estimation and control systems is considered. We model sensor measurement and transmission instances using jumps between states of a continuous-time Markov chain. We introduce a cost…
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…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…
We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…
Strong and weak simulation relations have been proposed for Markov chains, while strong simulation and strong probabilistic simulation relations have been proposed for probabilistic automata. However, decision algorithms for strong and weak…
Network models have been popular for modeling and representing complex relationships and dependencies between observed variables. When data comes from a dynamic stochastic process, a single static network model cannot adequately capture…
We establish results for the first sensitivity analysis of the stochastic fluid models (SFMs). We derive expressions for the sensitivity analysis of the key stationary and transient (time-dependent) quantities of this class of models. We…
We present a novel probabilistic deep learning approach, the 'Stochastic Latent Transformer' (SLT), designed for the efficient reduced-order modelling of stochastic partial differential equations. Stochastically driven flow models are…