Towards Machine Wald

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 \emph{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. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Genome sequencing reveals loci under artificial selection that underlie disease phenotypes in the laboratory rat

Large numbers of inbred laboratory rat strains have been developed for a range of complex disease phenotypes. To gain insights into the evolutionary pressures underlying selection for these phenotypes, we sequenced the genomes of 27 rat strains, including 11 models of hypertension, diabetes, and insulin resistance, along with their respective control strains. Altogether, we identified more than 13 million single-nucleotide variants, indels, and structural variants across these rat strains. Analysis of strain-specific selective sweeps and gene clusters implicated genes and pathways involved in cation transport, angiotensin production, and regulators of oxidative stress in the development of cardiovascular disease phenotypes in rats. Many of the rat loci that we identified overlap with previously mapped loci for related traits in humans, indicating the presence of shared pathways underlying these phenotypes in rats and humans. These data represent a step change in resources available for evolutionary analysis of complex traits in disease models