Related papers: Generalized mutual information and their reference…

Between Bayesian and frequentist inference, it's commonly believed that the former is for cases where one has a prior and the latter is for cases where one has no prior. But the prior/no-prior classification isn't exhaustive, and most…

There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…

We examine the connection between training error and generalization error for arbitrary estimating procedures, working in an overparameterized linear model under general priors in a Bayesian setup. We find determining factors inherent to…

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 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 are interested in learning data-driven representations that can generalize well, even when trained on inherently biased data. In particular, we face the case where some attributes (bias) of the data, if learned by the model, can severely…

A generalized information formula related to logical probability and fuzzy set is deduced from the classical information formula. The new information measure accords with to Popper's criterion for knowledge evolution very much. In…

A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…

Bayesian inference in generalized linear models requires a prior on the coefficient vector $\beta$. Practitioners naturally reason about response probabilities at specific covariate values, not about abstract log-odds parameters. We develop…

The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable…

In Bayesian analysis, reference priors are widely recognized for their objective nature. Yet, they often lead to intractable and improper priors, which complicates their application. Besides, informed prior elicitation methods are penalized…

Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider…

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…

Priors allow us to robustify inference and to incorporate expert knowledge in Bayesian hierarchical models. This is particularly important when there are random effects that are hard to identify based on observed data. The challenge lies in…

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…

Following the critical review of Seaman et al. (2012), we reflect on what is presumably the most essential aspect of Bayesian statistics, namely the selection of a prior density. In some cases, Bayesian inference remains fairly stable under…

In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…

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…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

We investigate the sets of joint probability distributions that maximize the average multi-information over a collection of margins. These functionals serve as proxies for maximizing the multi-information of a set of variables or the mutual…