相关论文: Bayes procedures for adaptive inference in inverse…

In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues.…

Supremum norm loss is intuitively more meaningful to quantify function estimation error in statistics. In the context of multivariate nonparametric regression with unknown error, we propose a Bayesian procedure based on spike-and-slab prior…

We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g., ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric…

We study the performance of nonparametric Bayes procedures for one-dimensional diffusions with periodic drift. We improve existing convergence rate results for Gaussian process (GP) priors with fixed hyper parameters. Moreover, we exhibit…

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…

We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…

Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…

This paper presents a comprehensive analysis of hyperparameter estimation within the empirical Bayes framework (EBF) for sparse learning. By studying the influence of hyperpriors on the solution of EBF, we establish a theoretical connection…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…

The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…

For ill-posed inverse problems, a regularised solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set the solutions, as other posterior estimates can be used as a solution…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian)…

We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…

A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…