Related papers: A Savage-Like Axiomatization for Nonstandard Expec…
Granger causal inference is a contentious but widespread method used in fields ranging from economics to neuroscience. The original definition addresses the notion of causality in time series by establishing functional dependence…
In earlier work, we introduced the framework of language-based decisions, the core idea of which was to modify Savage's classical decision-theoretic framework by taking actions to be descriptions in some language, rather than functions from…
Data analyses typically rely upon assumptions about missingness mechanisms that lead to observed versus missing data. When the data are missing not at random, direct assumptions about the missingness mechanism, and indirect assumptions…
An axiomatic characterization of Nash equilibrium is provided for games in normal form. The Nash equilibrium correspondence is shown to be fully characterized by four simple and intuitive axioms, two of which are inspired by contraction and…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…
The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as…
The Allais and Ellsberg paradoxes show that the expected utility hypothesis and Savage's Sure-Thing Principle are violated in real life decisions. The popular explanation in terms of 'ambiguity aversion' is not completely accepted. On the…
We provide a general theoretical analysis of expected out-of-sample utility, also referred to as decision-theoretic classification, for non-decomposable binary classification metrics such as F-measure and Jaccard coefficient. Our key result…
We use the theory of defaults and their meaning of [GS16] to develop (the outline of a) new theory of argumentation.
The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a…
The random utility model (RUM, McFadden and Richter, 1990) has been the standard tool to describe the behavior of a population of decision makers. RUM assumes that decision makers behave as if they maximize a rational preference over a…
We study a dynamic random utility model that allows for consumption dependence. We axiomatically analyze this model and find insights that allow us to distinguish between behavior that arises due to consumption dependence and behavior that…
This paper assumes each individual in society has a random discount factor and assesses an intertemporal project using rank-dependent expected utility theory. We consider both the ex ante and the ex post approaches. For the former, we show…
Supervised learning has gone beyond the expected risk minimization framework. Central to most of these developments is the introduction of more general aggregation functions for losses incurred by the learner. In this paper, we turn towards…
Ramsey (1926) sketches a proposal for measuring the subjective probabilities of an agent by their observable preferences, assuming that the agent is an expected utility maximizer. I show how to extend the spirit of Ramsey's method to a…
This book presents our case in defense of a constructivist epistemological framework and the use of compatible statistical theory and inference tools. The basic metaphor of decision theory is the maximization of a gambler's expected…
The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that…
The game-theoretic notion of the semivalue offers a popular framework for credit attribution and data valuation in machine learning. Semivalues have been proposed for a variety of high-stakes decisions involving data, such as determining…
This paper proposes a decision theory for a symbolic generalization of probability theory (SP). Darwiche and Ginsberg [2,3] proposed SP to relax the requirement of using numbers for uncertainty while preserving desirable patterns of…