Scientific Computation of Optimal Statistical Estimators
Abstract
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 estimators/models 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 13, 2015
- Accession Number
- ADA622663
Entities
People
- Houman Owhadi
Organizations
- California Institute of Technology