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We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the…
A new approach for uncertainty management for fuzzy, rule based decision support systems is proposed: The domain expert's knowledge is expressed by a set of rules that frequently refer to vague and uncertain propositions. The certainty of…
We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B),…
Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and…
An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher's fiducial argument have similar objectives, but a…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…
This paper addresses a significant gap in explainable AI: the necessity of interpreting epistemic uncertainty in model explanations. Although current methods mainly focus on explaining predictions, with some including uncertainty, they fail…
The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal…
In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…
An agent is a misspecified Bayesian if she updates her belief using Bayes' rule given a subjective, possibly misspecified model of her signals. This paper shows that a belief sequence is consistent with misspecified Bayesian updating if and…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and…
This paper examines the accuracy of the PROSPECTOR model for uncertain reasoning. PROSPECTOR's solutions for a large number of computer-generated inference networks were compared to those obtained from probability theory and minimum…
We characterize common assumption of rationality of 2-person games within an incomplete information framework. We use the lexicographic model with incomplete information and show that a belief hierarchy expresses common assumption of…
The fundamental challenge of drawing causal inference is that counterfactual outcomes are not fully observed for any unit. Furthermore, in observational studies, treatment assignment is likely to be confounded. Many statistical methods have…
Model selection and assessment with incomplete data pose challenges in addition to the ones encountered with complete data. There are two main reasons for this. First, many models describe characteristics of the complete data, in spite of…
What does it mean to say that, for example, the probability for rain tomorrow is between 20% and 30%? The theory for the evaluation of precise probabilistic forecasts is well-developed and is grounded in the key concepts of proper scoring…
This paper presents an advance in the direction of working with probabilities in a paracomplete setting using Logics of Formal Undeterminedness (LFUs). The undeterminedness is interpreted here as missing evidence. A theorem of total…
This paper advocates the usefulness of new theories of uncertainty for the purpose of modeling some facets of uncertain knowledge, especially vagueness, in AI. It can be viewed as a partial reply to Cheeseman's (among others) defense of…