Consider rolling a die with k sides, labeled a1, a2, ..., and ak, respectively. Let P(aj) be the ‘probability’ that a particular side aj appears after rolling the die. Before attempting to calculate P(aj), it is necessary to clarify the meaning of the word ‘probability’. In other words, we must specify what the number P(aj) quantifies. In statistics, the concept of ‘probability’ is formally int...

the differential information literature in economics and game theory? Why has the those posteriors are derived by updating the common prior. Perhaps the most world can be generated by conditioning by Bayes rule. If there are many. Find a weak perfect bayesian equilibrium (strategies and beliefs) where the be arbitrary (and thus don't have to be according to Bayesian updating) but I am under Bro...

Statistical decision theory (SDT) and Bayesian decision theory (BDT) are closely related mathematical frameworks used to model ideal performance in a wide range of visual and motor tasks. Their elements (gain function, likelihood, prior) are readily interpretable in terms of information available to the observer. We briefly describe SDT and BDT and then review recent work employing them as mode...

We present a computational framework for Theory of Mind (ToM): the human ability to make joint inferences about the unobservable beliefs and preferences underlying the observed actions of other agents. These mental state attributions can be understood as Bayesian inferences in a probabilistic generative model for rational action, or planning under uncertain and incomplete information, formalize...

Consider rolling a die with k sides, labeled a1, a2, ..., and ak, respectively. Let P(aj) be the ‘probability’ that a particular side aj appears after rolling the die. Before attempting to calculate P(aj), it is necessary to clarify the meaning of the word ‘probability’. In other words, we must specify what the number P(aj) quantifies. In statistics, the concept of ‘probability’ is formally int...

Consider rolling a die with k sides, labeled a1, a2, ..., and ak, respectively. Let P(aj) be the ‘probability’ that a particular side aj appears after rolling the die. Before attempting to calculate P(aj), it is necessary to clarify the meaning of the word ‘probability’. In other words, we must specify what the number P(aj) quantifies. In statistics, the concept of ‘probability’ is formally int...

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 ...