相关论文: Efficient Bayesian estimation and uncertainty quan…
Often the regression function appearing in fields like economics, engineering, biomedical sciences obeys a system of higher order ordinary differential equations (ODEs). The equations are usually not analytically solvable. We are interested…
Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\bm\theta$ of physical significance…
Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
We propose a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. For our new Bayesian approach, we first adjust the prior distributions of the conditional mean functions, and then correct…
Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…
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…
Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…
Ordinary differential equations (ODEs) are a mathematical model used in many application areas such as climatology, bioinformatics, and chemical engineering with its intuitive appeal to modeling. Despite ODE's wide usage in modeling, the…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…
We provide a comprehensive semi-parametric study of Bayesian partially identified econometric models. While the existing literature on Bayesian partial identification has mostly focused on the structural parameter, our primary focus is on…
This paper introduces a quasi-Bayesian method that integrates frequentist nonparametric estimation with Bayesian inference in a two-stage process. Applied to an endogenous discrete choice model, the approach first uses kernel or sieve…
Deep learning methods continue to have a decided impact on machine learning, both in theory and in practice. Statistical theoretical developments have been mostly concerned with approximability or rates of estimation when recovering…
We propose a new, two-step empirical Bayes-type of approach for neural networks. We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional…
We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…
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…
This is a review of asymptotic and non-asymptotic behaviour of Bayesian methods under model specification. In particular we focus on consistency, i.e. convergence of the posterior distribution to the point mass at the best parametric…
Bayesian inference provides a principled framework for probabilistic reasoning. If inference is performed in two steps, uncertainty propagation plays a crucial role in accounting for all sources of uncertainty and variability. This becomes…