Scientific Computation of Optimal Statistical Estimators
Final performance rept. 1 Aug 2012-31 Jul 2015
CALIFORNIA INST OF TECH PASADENA
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The past century has seen a steady increase in the need of estimating and predicting complex systems and making possibly critical decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed by humans because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations.With the purpose of addressing this problem this program has developed 1 the foundations of a rigorous framework for the scientific computation of optimal statistical estimatorsmodels and 2 the required calculus enabling the reduction of optimization problems over measures over spaces of measures and functions. Two highlights of the work accomplished consist of 1 the application of the calculus to the identification of brittleness in Bayesian inference and 2 the application of the framework to the automated identification of scalable linear solvers for PDEs with rough coefficients.
- Statistics and Probability
- Operations Research