Related papers: Bayesian Predictive Densities Based on Latent Info…
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…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
We define {\em predictive information} $I_{\rm pred} (T)$ as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times $T$: $I_{\rm…
Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
Two data-dependent information metrics are developed to quantify the information of the prior and likelihood functions within a parametric Bayesian model, one of which is closely related to the reference priors from Berger, Bernardo, and…
Diffusion models rely on a high-dimensional latent space of initial noise seeds, yet it remains unclear whether this space contains sufficient structure to predict properties of the generated samples, such as their classes. In this work, we…
Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and…
We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…
The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…
Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…
We reveal the relations between the conditional normalized maximum likelihood (CNML) distributions and Bayesian predictive densities based on the latent information priors (LIPs). In particular, CNML3, which is one type of CNML…
Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions…
The causal discovery of Bayesian networks is an active and important research area, and it is based upon searching the space of causal models for those which can best explain a pattern of probabilistic dependencies shown in the data.…
We investigate shrinkage priors for constructing Bayesian predictive distributions. It is shown that there exist shrinkage predictive distributions asymptotically dominating Bayesian predictive distributions based on the Jeffreys prior or…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…
We distinguish two questions (i) how much information does the prior contain? and (ii) what is the effect of the prior? Several measures have been proposed for quantifying effective prior sample size, for example Clarke [1996] and Morita et…
We consider Bayesian shrinkage predictions for the Normal regression problem under the frequentist Kullback-Leibler risk function. Firstly, we consider the multivariate Normal model with an unknown mean and a known covariance. While the…