相关论文: Martingale Posterior Predictive Coherence: Hausdor…

Let X and Y be an m-dimensional F-semimartingale and an n-dimensional H-semimartingale respectively on the same probability space, both enjoying the strong predictable representation property. We propose a martingale representation result…

The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are…

Let $(S_0,S_1,...)$ be a supermartingale relative to a nondecreasing sequence of $\sigma$-algebras $H_{\le0},H_{\le1},...$, with $S_0\le0$ almost surely (a.s.) and differences $X_i:=S_i-S_{i-1}$. Suppose that $X_i\le d$ and $\mathsf…

Federated Bayesian neural networks require fixing a prior on the model parameters together with a likelihood. Eliciting meaningful priors on the weight space of modern overparameterized models is notoriously difficult, and misspecification…

A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data…

The classical condition on the existence of uniformly exponentially consistent tests for testing the true density against the complement of its arbitrary neighborhood has been widely adopted in study of asymptotics of Bayesian nonparametric…

We develop a framework for the operationalization of models and parameters by combining de Finetti's representation theorem with a conditional form of Sanov's theorem. This synthesis, the tilted de Finetti theorem, shows that conditioning…

We introduce scalable algorithms for online learning of neural network parameters and Bayesian sequential decision making. Unlike classical Bayesian neural networks, which induce predictive uncertainty through a posterior over model…

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…

In inference problems involving a multi-dimensional parameter $\theta$, it is often natural to consider decision rules that have a risk which is invariant under some group $G$ of permutations of $\theta$. We show that this implies that the…

Bayesian inference provides principled uncertainty quantification but is often limited by the challenges of prior and likelihood elicitation. The martingale posterior (MGP) (Fong et al., 2023) offers an alternative by replacing these…

Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a…

The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…

Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…

We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…

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…

In Bayesian multilevel models, the data are structured in interconnected groups, and their posteriors borrow information from one another due to prior dependence between latent parameters. However, little is known about the behaviour of the…

In the standard Bayesian framework data are assumed to be generated by a distribution parametrized by $\theta$ in a parameter space $\Theta$, over which a prior distribution $\pi$ is given. A Bayesian statistician quantifies the belief that…

Mixtures of product distributions are a powerful device for learning about heterogeneity within data populations. In this class of latent structure models, de Finetti's mixing measure plays the central role for describing the uncertainty…

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…