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In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for…
Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…
Restricted Boltzmann machines (RBMs) are powerful machine learning models, but learning and some kinds of inference in the model require sampling-based approximations, which, in classical digital computers, are implemented using expensive…
We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a…
Sequential Monte Carlo has become a standard tool for Bayesian Inference of complex models. This approach can be computationally demanding, especially when initialized from the prior distribution. On the other hand, deter-ministic…
An efficient technique to simulate turbulent particle-laden flow at high mass loadings within the four-way coupled simulation regime is presented. The technique implements large eddy simulation, discrete phase simulation, a deterministic…
Diffusion bridge models in both continuous and discrete state spaces have recently become powerful tools in the field of generative modeling. In this work, we leverage the discrete state space formulation of bridge matching models to…
The unbalanced Schr\"odinger bridge problem (uSBP) seeks to interpolate between a probability measure $\rho_0$ and a sub-probability measure $\rho_T$ while minimizing KL divergence to a reference measure $\mathbf{R}$ on a path space. In…
In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity…
Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
We introduce a novel discretization scheme for Wasserstein gradient flows that involves successively computing Schr\"{o}dinger bridges with the same marginals. This is different from both the forward/geodesic approximation and the…
Nonintersecting Brownian bridges on the unit circle form a determinantal stochastic process exhibiting random matrix statistics for large numbers of walkers. We investigate the effect of adding a drift term to walkers on the circle…
A numerical tool relying on sharp Immersed Boundary Method (IBM) is developed for the analysis of aerospace applications. The method, which is conceived for application using segregated solvers relying on implicit time discretization, uses…
Diffusion through semipermeable structures arises in a wide range of processes in the physical and life sciences. Examples at the microscopic level range from artificial membranes for reverse osmosis to lipid bilayers regulating molecular…
We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: (1) a scale mixture of normals with respect to an alpha-stable random…
We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem…
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which…
The problem of detecting a single anomalous process among multiple independent processes is considered. Under a constraint on the number of processes that can be probed simultaneously, the decision maker should decide which processes to…