Empirical Bayes methods for Gaussian compound decision problems involving longitudinal data are considered. The new convex optimization formulation of the nonparametric (Kiefer-Wolfowitz) maximum likelihood estimator for mixture models is employed to construct nonparametric Bayes rules for...

High ratios of working age to dependent population can yield a increases the rate of economic growth. We estimate the parameters model with a cross section of countries over the period 1960 to 1980 inclusion of age structure improves the model’s forecasts for the period that including age...

We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space of parameters that describe statistical mechanics...

Recent experiments involving a relatively large population of neurons have shown a very significant amount of higher-order correlations. However, little is known of how these affect the integration and firing behavior of a population of neurons beyond the second order statistics. To investigate...

The introduction of a metric onto the space of parameters in models in statistical mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrisation, the scalar curvature, R, plays a central role. A non-interacting model has a flat geometry (R=0), while R...

An information-geometrical foundation is established for the deformed exponential families of probability distributions. Two different types of geometrical structures, an invariant geometry and a flat geometry, are given to a manifold of a deformed exponential family. The two different...