# Towards Machine Wald

arXiv: https://arxiv.org/abs/1508.02449 · HTML: https://mlsanity.com/paper/1508.02449/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2015.

## Built on by (most cited first, 4 of 4)

- [Experimental Design for Linear Functionals in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.13627/) (2022)
- [Uncertainty Quantification of the 4th kind; optimal posterior accuracy-uncertainty tradeoff with the minimum enclosing ball](https://mlsanity.com/paper/2108.10517/) (2021)
- [Aggregation of Pareto optimal models](https://mlsanity.com/paper/2112.04161/) (2021)
- [Position: Artificial Intelligence Needs Meta Intelligence -- the Case for Metacognitive AI](https://mlsanity.com/paper/2605.15567/) (2026)

## Abstract (arXiv)

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. Indeed enabling computers to think as 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.