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Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the…
We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…
The weak-field approximation is one of the simplest models that allows us to relate the observed polarization induced by the Zeeman effect with the magnetic field vector present on the plasma of interest. It is usually applied for…
Generalized linear models (GLMs) are routinely used for modeling relationships between a response variable and a set of covariates. The simple form of a GLM comes with easy interpretability, but also leads to concerns about model…
We present a Bayesian method for estimating instrumental noise parameters and propagating noise uncertainties within the global BeyondPlanck Gibbs sampling framework, and apply this to Planck Low Frequency Instrument (LFI) time-ordered…
We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
The extraction of any physical information from quasielastic neutron scattering spectra is generally done by fitting a model to the data by means of chi-square minimization procedure. However, as pointed out by the pioneering work of D.S.…
Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…
We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including…
We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…
An understanding of how input parameter uncertainty in the numerical simulation of physical models leads to simulation output uncertainty is a challenging task. Common methods for quantifying output uncertainty, such as performing a grid or…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…
The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the…
Being able to rigorously quantify the uncertainties in reaction models is crucial to moving this field forward. Even though Bayesian methods are becoming increasingly popular in nuclear theory, they are yet to be implemented and applied in…
Estimation of parameters of a diffusion based on discrete time observations poses a difficult problem due to the lack of a closed form expression for the likelihood. From a Bayesian computational perspective it can be casted as a missing…
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…