Newcomb's paradox highlights an apparent conflict involving the axioms of game theory. It concerns a game in which you choose to take either one or both of two closed boxes. However before you choose, a prediction algorithm deduces your choice, and fills the two boxes based on that deduction. The paradox is that game theory appears to provide two conflicting recommendations for what choice you ...

Under very general assumptions we show that Vafa-Witten theorem on vector symmetries in vector-like theories can be extended to some physically relevant gauge theories with non-positive definite integration measure as QCD with a Θ-vacuum term.

A two-factor experiment with interaction between factors wherein observations follow an Inverse Gaussian model is considered. Analysis of the experiment is approached via an empirical Bayes procedure. The conjugate family of prior distributions is considered. Bayes and empirical Bayes estimators are derived. Application of the procedure is illustrated on a data set, which has previously been an...

Those who study classiication theory, whether it be in the form of statistical pattern recognition, syntactical pattern recognition, or neural approaches to classiication are aware of the recent achievements and advances of their elds. For example names such as Bayes, Fisher, Wald, Fu, and Rosenblatt are well known for their pioneering contributions to classiication theory. However, few are awa...

Abstract. This paper clarifies the generalization errors of Bayes and Gibbs estimations in non-identifiable statistical models based on algebraic geometry and empirical process theory. First, the concrete results are proven for statistical models with normal crossing singularities. Second, they are generalized for all models by using Hironaka’s desingularization theorem. The Bayes generalizatio...

We present a general framework for representing belief-revision rules and use it to characterize Bayes’s rule as a classical example and Je¤rey’s rule as a non-classical one. In Je¤rey’s rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes’s rule, but a new assignment of probabilities to some events. Despite their di¤erences, Bayes’s and J...

By defining attack-defense action sequence and utility function of both sides, combine with dynamic Bayes game theory to analyze the confrontation and interdependence between the two agents’ strategies. Dynamic Bayes attack-defense game model can describe each possible strategy in every stage. This paper proposes the construction method of game extensive form by utilizing attack-defense confron...

This paper states necessary and sufficient conditions for the existence, uniqueness, and updating according to Bayes’ rule, of subjective probabilities representing individuals’ beliefs. The approach is preference based, and the result is an axiomatic subjective expected utility model of Bayesian decision making under uncertainty with statedependent preferences. The theory provides foundations ...