Related papers: Bayesian inference for nonlinear inverse problems

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…

In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…

Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…

Uncertainty quantification is central to many applications of causal machine learning, yet principled Bayesian inference for causal effects remains challenging. Standard Bayesian approaches typically require specifying a probabilistic model…

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further…

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…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…

Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters…

Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…

We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…

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…

We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…

We present a parametric deterministic formulation of Bayesian inverse problems with input parameter from infinite dimensional, separable Banach spaces. In this formulation, the forward problems are parametric, deterministic elliptic partial…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies…