Related papers: Ambiguity and Partial Bayesian Updating
How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive…
Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior…
This paper focuses on probability updates in multiply-connected belief networks. Pearl has designed the method of conditioning, which enables us to apply his algorithm for belief updates in singly-connected networks to multiply-connected…
Is it possible to make statistical inference broadly accessible to non-statisticians without sacrificing mathematical rigor or inference quality? This paper describes BayesDB, a probabilistic programming platform that aims to enable users…
Bayesian implementation concerns decision making problems when agents have incomplete information. This paper proposes that the traditional sufficient conditions for Bayesian implementation shall be amended by virtue of a quantum Bayesian…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…
Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
We explore the issue of refining an existent Bayesian network structure using new data which might mention only a subset of the variables. Most previous works have only considered the refinement of the network's conditional probability…
Conformal prediction has emerged as a popular technique for facilitating valid predictive inference across a spectrum of machine learning models, under minimal assumption of exchangeability. Recently, Hoff (2023) showed that full conformal…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
Learning a sequence of tasks without access to i.i.d. observations is a widely studied form of continual learning (CL) that remains challenging. In principle, Bayesian learning directly applies to this setting, since recursive and one-off…
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…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
When sample data are governed by an unknown sequence of independent but possibly non-identical distributions, the data-generating process (DGP) in general cannot be perfectly identified from the data. For making decisions facing such…
I propose a framework for an agent to change its probabilistic beliefs when a new piece of propositional information $\alpha$ is observed. Traditionally, belief change occurs by either a revision process or by an update process, depending…
Bayesian inference systems should be able to explain their reasoning to users, translating from numerical to natural language. Previous empirical work has investigated the correspondence between absolute probabilities and linguistic…
Quantifying uncertainty and updating reliability are essential for ensuring the safety and performance of engineering systems. This study develops a hierarchical Bayesian modeling (HBM) framework to quantify uncertainty and update…
Conditioning is the generally agreed-upon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of cross-entropy minimization,…
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…