The aim of the present paper is to obtain Bayes estimators for the oospring mean of a simple branching process with a power series oospring probability distribution. We study the sensitivity behavior of the obtained estimators with respect to the choice of the loss function. We propose a minimax criterion using the Bayes risk for ranking the eeectiveness (in the sense of robustness) of the loss...

This paper presents a data mining project that generated Bayesian models to assess risk of corruption of federal management units. With thousands of extracted features related to corruptibility, the data were processed using techniques like correlation analysis and variance per class. We also compared two different discretization methods: Minimum Description Length Principle (MDLP) and Class-At...

Recall that in Theorem 2.1, we analyzed empirical risk minimization with a finite hypothesis class F , i.e., |F| < +∞. Here, we will prove results for possibly infinite hypothesis classes. Although the PAC-Bayes framework is far more general, we will concentrate of the prediction problem as before, i.e., (∀f ∈ F) f : X → Y. Also, note that Theorem 2.1 could have been stated in a more general fa...

Recall that in Theorem 2.1, we analyzed empirical risk minimization with a finite hypothesis class F , i.e., |F| < +∞. Here, we will prove results for possibly infinite hypothesis classes. Although the PAC-Bayes framework is far more general, we will concentrate of the prediction problem as before, i.e., (∀f ∈ F) f : X → Y. Also, note that Theorem 2.1 could have been stated in a more general fa...

In this paper we survey the Bayes Risk Consistency of various Large Margin Binary Classifiers. Many classification algorithms minimize a tractable convex surrogate φ of the 0-1 loss function. For e.g. the SVM (Support Vector Machine) and AdaBoost, which minimize the hinge loss and the exponential loss respectively. By imposing some sort of regularization conditions, it is possible to demonstrat...

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...

This paper shows how a multivariate Bayes estimator can be adjusted to satisfy a set of linear constraints. In the direct approach, the constraint is enforced by a restriction on the class of admissible estimators. In an alternative approach, the constraint is merely encouraged by a mixed risk function which penalises misbalance between the estimator and the constraint. The adjustment to the op...