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This paper proposes a belief-based framework for social norms in environments where individuals choose a single action. Relaxing the assumption that the appropriateness standard is common knowledge, the framework allows individuals to be…
By probabilistic logic I mean a normative theory of belief that explains how a body of evidence affects one's degree of belief in a possible hypothesis. A new axiomatization of such a theory is presented which avoids a finite additivity…
We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random…
We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…
The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of…
Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
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…
People often deviate from expected utility theory when making risky and intertemporal choices. While the effects of probabilistic risk and time delay have been extensively studied in isolation, their interplay and underlying theoretical…
In some real world information fusion situations, time critical decisions must be made with an incomplete information set. Belief function theories (e.g., Dempster-Shafer theory of evidence, Transferable Belief Model) have been shown to…
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…
Several scientific fields including psychology are undergoing a replication crisis. There are many reasons for this problem, one of which is a misuse of p-values. There are several alternatives to p-values, and in this paper we describe a…
Reasoning about uncertainty is vital in many real-life autonomous systems. However, current state-of-the-art planning algorithms cannot either reason about uncertainty explicitly, or do so with a high computational burden. Here, we focus on…
This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions,…