Thermodynamic formalism and Uncertainty Quantification
Luc Rey-Bellet

Imagine a stochastic model  subject to uncertainty  (e.g. model
miss-specifcation or uncertainty in the parameters in the models). We are
particularly interested in  large systems in a long-time, steady state, 
regime.  We provide new uncertainty bounds on statistical estimators 
(expected value of observable, variance,  probability of rare event) using 
relative entropy, relative renyi entropy and Gibbs-type variational principles.