All mathematical models of real-world phenomena contain parameters that need to be estimated from measurements, either for realistic predictions or simply to understand the characteristics of the model. Bayesian statistics provides a framework for parameter estimation in which uncertainties about models and measurements are translated into uncertainties in estimates of parameters. This paper pr...

Due to their many applications, large Bayesian games have been a subject of growing interest in game theory and related fields. But to a large extent, models (1) have been restricted to one-shot interaction, (2) are based on an assumption that player types are independent and (3) assume that the number of players is known. The current paper develops a general theory of Bayesian repeated large g...

The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are ...

Due to their many applications, large Bayesian games have been a subject of growing interest in game theory and related fields. But to a large extent, models (1) have been restricted to one-shot interaction, (2) are based on an assumption that player types are independent and (3) assume that the number of players is known. The current paper develops a general theory of Bayesian repeated large g...