Related papers: A categorical foundation for Bayesian probability
Composite likelihoods are increasingly used in applications where the full likelihood is analytically unknown or computationally prohibitive. Although the maximum composite likelihood estimator has frequentist properties akin to those of…
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…
Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…
This paper deals with the problem of quantifying the approximation a probability measure by means of an empirical (in a wide sense) random probability measure, depending on the first n terms of a sequence of random elements. In Section 2,…
The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and…
Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability…
In this article, we study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with…
Random integral mappings $I^{h,r}_{(a,b]}$ give isomorphisms between the sub-semigroups of the classical $(ID, \ast)$ and the free-infinite divisible $(ID,\boxplus)$ probability measures. This allows us to introduce new examples of such…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…
We introduce a comprehensive Bayesian multivariate predictive inference framework. The basis for our framework is a hierarchical Bayesian model, that is a mixture of finite Polya trees corresponding to multiple dyadic partitions of the unit…
In Bayesian classification, it is important to establish a probabilistic model for each class for likelihood estimation. Most of the previous methods modeled the probability distribution in the whole sample space. However, real-world…
A probabilistic technique for the joint estimation of background and sources with the aim of detecting faint and extended celestial objects is described. Bayesian probability theory is applied to gain insight into the coexistence of…
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space,…
Given positive measures $\nu,\mu$ on an arbitrary measurable space $(\Omega, \mathcal F)$, we construct a sequence of finite partitions $(\pi_n)_n$ of $(\Omega, \mathcal F)$ s.t. $$ \sum_{A\in \pi_n: \mu(A)>0} 1_{A} \frac{\nu(A)}{\mu(A)}…
Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…
A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger…
This article establishes general conditions for posterior consistency of Bayesian finite mixture models with a prior on the number of components. That is, we provide sufficient conditions under which the posterior concentrates on…
The following zero-sum game between nature and a statistician blends Bayesian methods with frequentist methods such as p-values and confidence intervals. Nature chooses a posterior distribution consistent with a set of possible priors. At…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…