Beyond Bayes

Hierarchical Bayes and Empirical Bayes. Mlii Method. 1.1 Hierarchical Bayesian Analysis

Hierarchical Bayes and Empirical Bayes are related by their goals, but quite different by the methods of how these goals are achieved. The attribute hierarchical refers mostly to the modeling strategy, while empirical is referring to the methodology. Both methods are concerned in specifying the distribution at prior level, hierarchical via Bayes inference involving additional degrees of hierarc...

Beyond Bayes.

Bayes, E-Bayes and Robust Bayes Premium Estimation and Prediction under the Squared Log Error Loss Function

In risk analysis based on Bayesian framework, premium calculation requires specification of a prior distribution for the risk parameter in the heterogeneous portfolio. When the prior knowledge is vague, the E-Bayesian and robust Bayesian analysis can be used to handle the uncertainty in specifying the prior distribution by considering a class of priors instead of a single prior. In th...

Bayes Correlated Equilibrium and the Comparison of Information Structures in Games * September 16 , 2013 Revised October

The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals beyond the given information structure is equivalent to the set of a version of incomplete information correlated equilibrium which we dub Bayes correlated equilibrium. A game of incomplete information can be decomposed into a basic game, given by act...

Estimation and beyond in the Bayes Universe. 1.1 Estimation

This implies that the Bayes risk is 0. The Bayes risk of δπ(X) can be calculated as repeated expectation in two ways, r(π, δπ) = EθEX|θ(θ − δπ(X)) = EXEθ|X(θ − δπ(X)). Thus, conveniently choosing either EθEX|θ or EXEθ|X and using the properties of conditional expectation we have, r(π, δπ) = EθEX|θθ2 −EθEX|θθδπ(X)−EXEθ|Xθδπ(X) + EXEθ|Xδ2 π(X) = EθEX|θθ2 −Eθθ[EX|θδπ(X)]− EXδπ(X)Eθ|Xθ + EXEθ|Xδ2 π...