Related papers: Unbiased simulation of rare events in continuous t…
Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…
In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…
We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…
We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm.…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Rare events are processes that occur upon the emergence of unlikely fluctuations. Unlike what their name suggests, rare events are fairly ubiquitous in nature, as the occurrence of many structural transformations in biology and material…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…
We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the…
We consider the development of unbiased estimators, to approximate the stationary distribution of Mckean-Vlasov stochastic differential equations (MVSDEs). These are an important class of processes, which frequently appear in applications…
We show that any application of the technique of unbiased simulation becomes perfect simulation when coalescence of the two coupled Markov chains can be practically assured in advance. This happens when a fixed number of iterations is high…
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…
With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…
In this article we consider a Monte Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can…
Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…