Convexity and Conditional Expectations

Conditional Expectations and Renormalization

In optimal prediction methods one estimates the future behavior of underresolved systems by solving reduced systems of equations for expectations conditioned by partial data; renormalization group methods reduce the number of variables in complex systems through integration of unwanted scales. We establish the relation between these methods for systems in thermal equilibrium, and use this relat...

Effective dynamics using conditional expectations

The question of coarse-graining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarse-grained variable ξ(x), where x describes the configuration of the system in a high-dimensional space R, and ξ is a smooth function with value in R (typically a reaction coordinate). It is well known that, given a Boltzmann-Gibbs di...

The Specification of Conditional Expectations

This paper explores different speciÞcations of conditional expectations. The most common speciÞcation, linear least squares, is contrasted with nonparametric techniques that make no assumptions about the distribution of the data. Nonparametric regression is successful in capturing some nonlinearities in Þnancial data, in particular, asymmetric responses of security returns to the direction and ...

DEA with efficiency classification preserving conditional convexity

Introduction to Conditional Probabilities and Expectations