Related papers: Reflecting about Selecting Noninformative Priors
We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…
Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach,…
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…
In the last months, due to the emergency of Covid-19, questions related to the fact of belonging or not to a particular class of individuals (`infected or not infected'), after being tagged as `positive' or `negative' by a test, have never…
The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly,…
The notion of confidence distributions is applied to inference about the parameter in a simple autoregressive model, allowing the parameter to take the value one. This makes it possible to compare to asymptotic approximations in both the…
Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…
We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected…
We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…
We explore the construction of nonsubjective prior distributions in Bayesian statistics via a posterior predictive relative entropy regret criterion. We carry out a minimax analysis based on a derived asymptotic predictive loss function and…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
We show that it can be suboptimal for Bayesian decision-making agents employing social learning to use correct prior probabilities as their initial beliefs. We consider sequential Bayesian binary hypothesis testing where each individual…
We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as…
Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when model misspecifications exist in prior and/or data distributions, the direct application of Bayes' rule…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…