Related papers: Dynamics of Bayesian Updating with Dependent Data …

Bayesian analyses are often performed using so-called noninformative priors, with a view to achieving objective inference about unknown parameters on which available data depends. Noninformative priors depend on the relationship of the data…

An agent is a misspecified Bayesian if she updates her belief using Bayes' rule given a subjective, possibly misspecified model of her signals. This paper shows that a belief sequence is consistent with misspecified Bayesian updating if and…

We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…

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…

We provide a reason for Bayesian updating, in the Bernoulli case, even when it is assumed that observations are independent and identically distributed with a fixed but unknown parameter $\theta_0$. The motivation relies on the use of loss…

Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic characterization that…

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of…

There is significant growth and interest in the use of synthetic data as an enabler for machine learning in environments where the release of real data is restricted due to privacy or availability constraints. Despite a large number of…

Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…

It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…

We study asymptotic properties of Bayesian multiple testing procedures and provide sufficient conditions for strong consistency under general dependence structure. We also consider a novel Bayesian multiple testing procedure and associated…

We consider generalized Bayesian inference on stochastic processes and dynamical systems with potentially long-range dependency. Given a sequence of observations, a class of parametrized model processes with a prior distribution, and a loss…

In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution $P_0$, which may not be in the support of the prior, we show that the posterior…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

In an ideal setting for Bayesian agents, a perfect description of the rules of the environment (i.e., the objective observation model) is available, allowing them to reason through the Bayesian posterior to update their beliefs in an…

Mixed data refers to a type of data in which variables can be of multiple types, such as continuous, discrete, or categorical. This data is routinely collected in various fields, including healthcare and social sciences. A common goal in…