Related papers: A pathwise inference method for the parameters of …
Diffusion models typically operate in the standard framework of generative modelling by producing continuously-valued datapoints. To this end, they rely on a progressive Gaussian smoothing of the original data distribution, which admits an…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…
In this article we consider a family of real-valued diffusion processes on the time interval $[0,1]$ indexed by their prescribed initial value $x \in \mathbb{R}$ and another point in space, $y \in \mathbb{R}$. We first present an…
We present a brief review on the Impulse Approximation method to study processes of scattering off composite particles. We first construct the model in a non-relativistic fashion that enables us to extend the model to a covariant Impulse…
Reflected diffusions in convex polyhedral domains arise in a variety of applications, including interacting particle systems, queueing networks, biochemical reaction networks and mathematical finance. Under suitable conditions on the data,…
Gaussian processes regression is applied to augment experimental data of transfer-path analysis (TPA) by known information about the underlying physical properties of the system under investigation. The approach can be used as an…
The transport of charged particles in various astrophysical environments permeated by magnetic fields is described in terms of a diffusion process, which relies on diffusion-tensor parameters generally inferred from Monte-Carlo simulations.…
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
We present a conditional diffusion model - ConDiSim, for simulation-based inference of complex systems with intractable likelihoods. ConDiSim leverages denoising diffusion probabilistic models to approximate posterior distributions,…
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…
Priors are essential for reconstructing images from noisy and/or incomplete measurements. The choice of the prior determines both the quality and uncertainty of recovered images. We propose turning score-based diffusion models into…
We propose a new perspective for the evaluation of matching procedures by considering the complexity of the function class they belong to. Under this perspective we provide theoretical guarantees on post-matching covariate balance through a…
Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.…
We suggest a rigorous definition of the pathwise flux across the boundary of a bounded open set for transient finite energy diffusion processes. The expectation of such a flux has the property of depending only on the current velocity $v$,…
Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as…
Cox proportional hazard regression model is a popular tool to analyze the relationship between a censored lifetime variable with other relevant factors. The semi-parametric Cox model is widely used to study different types of data arising…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of…
We consider a non-stationary Cox-Ingersoll-Ross process. We establish a sharp large deviation principle for the maximum likelihood estimator of its drift parameter.
We propose a scalable framework for inference in an inhomogeneous Poisson process modeled by a continuous sigmoidal Cox process that assumes the corresponding intensity function is given by a Gaussian process (GP) prior transformed with a…