Related papers: Coherence, Belief Expansion and Bayesian Networks
This paper will focus on the process of 'fusing' several observations or models of uncertainty into a single resultant model. Many existing approaches to fusion use subjective quantities such as 'strengths of belief' and process these…
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…
We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and…
Bayesian models of cognition hypothesize that human brains make sense of data by representing probability distributions and applying Bayes' rule to find the best explanation for available data. Understanding the neural mechanisms underlying…
In this paper, we are concerned with attributing meaning to the results of a Bayesian analysis for a problem which is sufficiently complex that we are unable to assert a precise correspondence between the expert probabilistic judgements of…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
Large language models (LLMs) are increasingly used as agents that interact with users and with the world. To do so successfully, LLMs must construct representations of the world and form probabilistic beliefs about them. To provide…
A Bayesian belief network models a joint distribution with an directed acyclic graph representing dependencies among variables and network parameters characterizing conditional distributions. The parameters are viewed as random variables to…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…
Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may ask whether composing the inversions of the component…
This paper presents a model of costly information acquisition where decision-makers can choose whether to elaborate information superficially or precisely. The former action is costless, while the latter entails a processing cost. Within…
This work studies the learning abilities of agents sharing partial beliefs over social networks. The agents observe data that could have risen from one of several hypotheses and interact locally to decide whether the observations they are…
The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…
Theory refinement is the task of updating a domain theory in the light of new cases, to be done automatically or with some expert assistance. The problem of theory refinement under uncertainty is reviewed here in the context of Bayesian…
Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian belief networks. By imposing additional assumptions about the nature of the probabilistic models represented in the belief networks, we derive…
Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They…
We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and…
Quantifying coherence has received increasing attention, and considerable work has been directed towards finding coherence measures. While various coherence measures have been proposed in theory, an important issue following is how to…