Related papers: Bayesian Inference for a Time-Fractional HIV Model…

This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…

The analysis of diffusion processes in real-world propagation scenarios often involves estimating variables that are not directly observed. These hidden variables include parental relationships, the strengths of connections between nodes,…

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…

Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…

Despite the recent development of methods dealing with partially observed epidemic dynamics (unobserved model coordinates, discrete and noisy outbreak data), limitations remain in practice, mainly related to the quantity of augmented data…

This study proposes a novel approach to quantifying uncertainties of constitutive relations inferred from noisy experimental data using inverse modelling. We focus on electrochemical systems in which charged species (e.g., Lithium ions) are…

Diffusion models have recently been shown to excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. A common framework uses task-agnostic unconditional models that are later…

Inverse problems are of great importance in astrophysics for deriving information about the physical characteristics of hot optically thin plasma sources from their EUV and X-ray spectra. We describe and test an iterative method developed…

Reliable estimation of spatio-temporal trends in population-level HIV incidence is becoming an increasingly critical component of HIV prevention policy-making. However, direct measurement is nearly impossible. Current, widely used models…

A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…

In the paper, we present a strategy for accelerating posterior inference for unknown inputs in time fractional diffusion models. In many inference problems, the posterior may be concentrated in a small portion of the entire prior support.…

Infectious disease dynamics operate across multiple biological scales, with within-host viral dynamics being a key driver of between-host transmission. However, while models that explicitly link these scales exist, none have been developed…

We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…

A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…

We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant…

Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates…

Modeling viral dynamics in HIV/AIDS studies has resulted in a deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear…

We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…

This paper studies the problem of distributed state estimation (DSE) over sensor networks on matrix Lie groups, which is crucial for applications where system states evolve on Lie groups rather than vector spaces. We propose a…