Related papers: An Axiomatic Framework for Belief Updates
This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes the pragmatic elements in the derivation. An epistemic notion of information is defined in…
Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that…
As large language models (LLMs) continue to demonstrate remarkable abilities across various domains, computer scientists are developing methods to understand their cognitive processes, particularly concerning how (and if) LLMs internally…
Methods for probability updating, of which Bayesian conditionalization is the most well-known and widely used, are modeling tools that aim to represent the process of modifying an initial epistemic state, typically represented by a prior…
Probabilistic epistemic argumentation allows for reasoning about argumentation problems in a way that is well founded by probability theory. Epistemic states are represented by probability functions over possible worlds and can be adjusted…
We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our…
While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the…
Robust belief revision methods are crucial in streaming data situations for updating existing knowledge or beliefs with new incoming evidence. Bayes conditioning is the primary mechanism in use for belief revision in data fusion systems…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
Belief and plausibility are weaker measures of uncertainty than that of probability. They are motivated by the situations when full probabilistic information is not available. However, information can also be contradictory. Therefore, the…
Transforming a random variable to improve its normality leads to a followup test for whether the transformed variable follows a normal distribution. Previous work has shown that the Anderson Darling test for normality suffers from…
Many variables in the social, physical, and biosciences, including neuroscience, are non-normally distributed. To improve the statistical properties of such data, or to allow parametric testing, logarithmic or logit transformations are…
In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and…
We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by…
The Cox proportional hazards model, commonly used in clinical trials, assumes proportional hazards. However, it does not hold when, for example, there is a delayed onset of the treatment effect. In such a situation, an acute change in the…
This paper studies implications of the consistency conditions among prior, posteriors, and information sets on introspective properties of qualitative belief induced from information sets. The main result reformulates the consistency…
Aumann's famous Agreeing to Disagree Theorem states that if a group of agents share a common prior, update their beliefs by Bayesian conditioning based on private information, and have common knowledge of their posterior beliefs regarding…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
Understanding how humans revise their beliefs in light of new information is crucial for developing AI systems which can effectively model, and thus align with, human reasoning. While theoretical belief revision frameworks rely on a set of…