Related papers: Adaptive Bayesian Estimation of Conditional Densit…

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the…

We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly…

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,…

Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is…

Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…

We develop a nonparametric Bayesian modeling approach to ordinal regression based on priors placed directly on the discrete distribution of the ordinal responses. The prior probability models are built from a structured mixture of…

In a smooth semi-parametric model, the marginal posterior distribution for a finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of any efficient point-estimator. The assertion…

Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density $f_0$ of its jump sizes, as well as of its intensity $\lambda_0.$ We take a Bayesian approach to the problem and…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. 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…

The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so…

We study nonparametric Bayesian inference for the intensity function of a covariate-driven point process. We extend recent results from the literature, showing that a wide class of Gaussian priors, combined with flexible link functions,…

To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper Schwartz's 1965 Kullback-Leibler condition is generalised to enable frequentist interpretation of convergence of posterior distributions…

Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…