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Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…

We propose an unsupervised anomaly detection approach based on a physics-informed diffusion model for multivariate time series data. Over the past years, diffusion model has demonstrated its effectiveness in forecasting, imputation,…

A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is…

Imitation learning with diffusion models has advanced robotic control by capturing the multi-modal action distributions. However, existing methods typically treat observations only as high-level conditions to the denoising network, rather…

A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the…

In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…

This paper investigates a financial market where returns depend on an unobservable Gaussian drift process. While the observation of returns yields information about the underlying drift, we also incorporate discrete-time expert opinions as…

A common challenge in the natural sciences is to disentangle distinct, unknown sources from observations. Examples of this source separation task include deblending galaxies in a crowded field, distinguishing the activity of individual…

Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…

Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…

As models of cognition grow in complexity and number of parameters, Bayesian inference with standard methods can become intractable, especially when the data-generating model is of unknown analytic form. Recent advances in simulation-based…

A distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel is considered. When the sensor measurements are decreasingly reliable as a function of the sensor index, the conditions on the…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

Partially-observed data collected by sampling methods is often being studied to obtain the characteristics of information diffusion networks. However, these methods usually do not consider the behavior of diffusion process. In this paper,…

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

We construct a generalization of the Ornstein-Uhlenbeck processes on the cone of covariance matrices endowed with the Log-Euclidean and the Affine-Invariant metrics. Our development exploits the Riemannian geometric structure of symmetric…

This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially-observed problem is reformulated into one with full observations, via a change of…

We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…