Related papers: A new axiomatization for likelihood gambles

There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…

Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…

In this paper we analyze two recent axiomatic approaches proposed by Dubois et al and by Giang and Shenoy to qualitative decision making where uncertainty is described by possibility theory. Both axiomtizations are inspired by von Neumann…

This paper investigates the dynamics of gambling and how they can affect risk-taking behavior in regions not explored by Kahneman and Tversky's Prospect Theory. Specifically, it questions why extreme outcomes do not fit the theory and…

In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.

When sample data are governed by an unknown sequence of independent but possibly non-identical distributions, the data-generating process (DGP) in general cannot be perfectly identified from the data. For making decisions facing such…

A decision maker observes the evolving state of the world while constantly trying to predict the next state given the history of past states. The ability to benefit from such predictions depends not only on the ability to recognize patters…

When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…

The paper introduces a new approach to theory of differential games in which entangled players try to predict and influence actions of their adversaries. The entanglement is generated be a joint probability density known by the players.…

This paper provides an analysis of different formal representations of beliefs in epistemic game theory. The aim is to attempt a synthesis of different structures of beliefs in the presence of indeterminate probabilities. Special attention…

Most positive and unlabeled data is subject to selection biases. The labeled examples can, for example, be selected from the positive set because they are easier to obtain or more obviously positive. This paper investigates how learning can…

This paper develops a theory of learning under ambiguity induced by the decision maker's beliefs about the collection of data correlated with the true state of the world. Within our framework, two classical results on Bayesian learning…

There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…

In recent years, there has been an increased need for the use of active systems - systems required to act automatically based on events, or changes in the environment. Such systems span many areas, from active databases to applications that…

Sequences of repeated gambles provide an experimental tool to characterize the risk preferences of humans or artificial decision-making agents. The difficulty of this inference depends on factors including the details of the gambles offered…

Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion -- almost everywhere computable randomness. A binary sequence…

We introduce a new updating rule, the conditional maximum likelihood rule (CML) for updating ambiguous information. The CML formula replaces the likelihood term in Bayes' rule with the maximal likelihood of the given signal conditional on…

We introduce a solution concept for extensive-form games of incomplete information in which players need not assign likelihoods to what they do not know about the game. This is embedded in a model in which players can hold multiple priors.…

The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…

In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…