相关论文: Bayes Sensitivity with Fisher-Rao Metric

We propose a geometric framework to assess global sensitivity in Bayesian nonparametric models for density estimation. We study sensitivity of nonparametric Bayesian models for density estimation, based on Dirichlet-type priors, to…

We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold of probability density functions. Under the square-root density representation, the…

Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…

It is well known that the Fisher information induces a Riemannian geometry on parametric families of probability density functions. Following recent work, we consider the nonparametric generalization of the Fisher geometry. The resulting…

Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…

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…

Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice.…

Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…

Parametric Bayesian modeling offers a powerful and flexible toolbox for machine learning. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we introduce a new class of…

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…

This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model.…

This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in…

Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity…

Although Bayesian methods are robust and principled, their application in practice could be limited since they typically rely on computationally intensive Markov Chain Monte Carlo algorithms for their implementation. One possible solution…

Bayesian networks are one of the most widely used classes of probabilistic models for risk management and decision support because of their interpretability and flexibility in including heterogeneous pieces of information. In any applied…

This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…

This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a…

We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated…

Fairness concerns are increasingly critical as machine learning models are deployed in high-stakes applications. While existing fairness-aware methods typically intervene at the model level, they often suffer from high computational costs,…

The Fisher-Rao distance between two probability distributions of a statistical model is defined as the Riemannian geodesic distance induced by the Fisher information metric. In order to calculate the Fisher-Rao distance in closed-form, we…