Related papers: Bayesian two-step estimation in differential equat…
Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…
Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…
The main goal of this paper is to study the parameter estimation problem, using the Bayesian methodology, for the drift coefficient of some linear (parabolic) SPDEs driven by a multiplicative noise of special structure. We take the spectral…
Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions.…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise,…
This paper brings a contribution to the Bayesian theory of nonparametric and semiparametric estimation. We are interested in the asymptotic normality of the posterior distribution in Gaussian linear regression models when the number of…
There has been significant progress in Bayesian inference based on sparsity-inducing (e.g., spike-and-slab and horseshoe-type) priors for high-dimensional regression models. The resulting posteriors, however, in general do not possess…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…
We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and…
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…
Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…
We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…
We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…
In this paper we study application of Le Cam's one-step method to parameter estimation in ordinary differential equations models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular…