Related papers: Integration based profile likelihood calculation f…
A profile likelihood ratio test is proposed for inferences on the index coefficients in generalized single-index models. Key features include its simplicity in implementation, invariance against parametrization, and exhibiting substantially…
The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
Nonlocally related partial differential equation (PDE) systems are useful in the analysis of a given PDE system. It is known that each local conservation law of a given PDE system systematically yields a nonlocally related system. In this…
Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
In this paper, we present solvable, convex formulations of $H_2$-optimal state estimation and state-feedback control problems for a general class of linear Partial Differential Equations (PDEs) with one spatial dimension. These convex…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
This paper focuses on designing a particle filter for randomly delayed measurements with an unknown latency probability. A generalized measurement model is adopted which includes measurements that are delayed randomly by an arbitrary but…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…
In many science and engineering settings, system dynamics are characterized by governing PDEs, and a major challenge is to solve inverse problems (IPs) where unknown PDE parameters are inferred based on observational data gathered under…
A characteristic of existing predictive process monitoring techniques is to first construct a predictive model based on past process executions, and then use it to predict the future of new ongoing cases, without the possibility of updating…
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
Valid statistical inference is challenging when the sample is subject to unknown selection bias. Data integration can be used to correct for selection bias when we have a parallel probability sample from the same population with some common…
In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…
Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…
Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…
This report presents the results of a partial differential equation (PDE)-based image enhancement algorithm, for dynamic range compression and illumination correction in the absence of the logarithmic function. The proposed algorithm…
We discuss methods for {\em a priori} selection of parameters to be estimated in inverse problem formulations (such as Maximum Likelihood, Ordinary and Generalized Least Squares) for dynamical systems with numerous state variables and an…