Related papers: Gaussian Approximations for Probability Measures o…
In this paper we derive lower bounds in minimax sense for estimation of the instantaneous volatility if the diffusion type part cannot be observed directly but under some additional Gaussian noise. Three different models are considered. Our…
We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the "true" solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and…
Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process,…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect…
We consider the problem of frequency estimation of the periodic signal multiplied by a stationary Gaussian process (Ornstein-Uhlenbeck) and observed in the presence of the white Gaussian noise. We show the consistency and asymptotic…
Estimating Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor distances between these samples.…
The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered.…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL)…
In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which include the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. We are interested in divergence…
We investigate Bayesian non-parametric inference of the $\Lambda$-measure of $\Lambda$-coalescent processes with recurrent mutation, parametrised by probability measures on the unit interval. We give verifiable criteria on the prior for…
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…
We continue the investigation of Bernstein-von Mises theorems for nonparametric Bayes procedures from [Ann. Statist. 41 (2013) 1999-2028]. We introduce multiscale spaces on which nonparametric priors and posteriors are naturally defined,…
We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the…
We propose a scalable inference algorithm for Bayes posteriors defined on a reproducing kernel Hilbert space (RKHS). Given a likelihood function and a Gaussian random element representing the prior, the corresponding Bayes posterior measure…
Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…
The Kullback-Leibler divergence or relative entropy is an information-theoretic measure between statistical models that play an important role in measuring a distance between random variables. In the study of complex systems, random fields…
Gaussian multiplicative noise is commonly used as a stochastic regularisation technique in training of deterministic neural networks. A recent paper reinterpreted the technique as a specific algorithm for approximate inference in Bayesian…