Enclose it or Lose it! Computer-aided Proofs in Statistics

Enclosure methods are a class of computer-aided proofs used in analysis. They are used increasingly to solve open problems in mathematics. The proposed project will use enclosure methods to address two open statistical decision problems: 1. rigorous parameter estimation in a chaotic statistical experiment, and 2. rigorous point estimation and exact posterior sampling in phylogenetics. To address these problems, we will adapt and extend recent developments in contractor programming, interval constraint propagation, algebraic statistical constraints and employ a novel mapped sub-paving arithmetic. A C++ class library that can harness UC’s super computing power for such computer-aided proofs will be made publicly available along with a database of solutions.