Related papers: Bayesian Predictive Density Estimation for a Chi-s…
We study empirical Bayes (EB) predictive density estimation in linear mixed models (LMMs) with large number of units, which induce a high dimensional random effects space. Focusing on Kullback Leibler (KL) risk minimization, we develop a…
The Bayesian nonparametric inference and Dirichlet process are popular tools in statistical methodologies. In this paper, we employ the Dirichlet process in hypothesis testing to propose a Bayesian nonparametric chi-squared goodness-of-fit…
Frequentist conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate the flexibility in criteria…
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…
When evaluating and comparing models using leave-one-out cross-validation (LOO-CV), the uncertainty of the estimate is typically assessed using the variance of the sampling distribution. Considering the uncertainty is important, as the…
The paper considers the distribution of a general linear combination of central and non-central chi-square random variables by exploring the branch cut regions that appear in the standard Laplace inversion process. Due to the original…
We propose information criteria that measure the prediction risk of a predictive density based on the Bayesian marginal likelihood from a frequentist point of view. We derive criteria for selecting variables in linear regression models,…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…
In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the…
We investigate Bayesian shrinkage methods for constructing predictive distributions. We consider the multivariate Normal model with a known covariance matrix and show that the Bayesian predictive density with respect to Stein's harmonic…
We propose a new model selection method, the posterior averaging information criterion, for Bayesian model assessment from a predictive perspective. The theoretical foundation is built on the Kullback-Leibler divergence to quantify the…
We have investigated a weighted chi-square distribution of the variable $\xi$ which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles $\phi_k=2\pi k/N$, where $k \in \{0,1,...,N-1\}$…
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.…
Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…
We consider in this paper the problem of sampling a high-dimensional probability distribution $\pi$ having a density with respect to the Lebesgue measure on $\mathbb{R}^d$, known up to a normalization constant $x \mapsto \pi(x)=…
Given a random sample from a distribution with density function that depends on an unknown parameter $\theta$, we are interested in accurately estimating the true parametric density function at a future observation from the same…
In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured,…
The Kullback-Leibler (KL) divergence is a foundational measure for comparing probability distributions. Yet in multivariate settings, its single value often obscures the underlying reasons for divergence, conflating mismatches in individual…