Certified Decisions

TL;DR

This paper introduces a framework for certified decisions that pairs recommended actions with probabilistic inferential guarantees, enabling safer decision-making under uncertainty.

Contribution

It develops a theory of certified decisions using P-certificates and E-certified decisions, linking hypothesis testing to risk-controlled decisions with formal guarantees.

Findings

P-certificates provide probabilistic loss bounds for decisions.

Minimax confidence set-based decisions are optimal for P-certificates.

E-certified decisions extend the framework to unbounded loss scenarios.

Abstract

Hypothesis tests and confidence intervals are ubiquitous in empirical research, yet their connection to subsequent decision-making is often unclear. We develop a theory of certified decisions that pairs recommended decisions with inferential guarantees. Specifically, we attach P-certificates -- upper bounds on loss that hold with probability at least $1-\alpha$ -- to recommended actions. We show that such certificates allow "safe," risk-controlling adoption decisions for ambiguity-averse downstream decision-makers. We further prove that it is without loss to limit attention to P-certificates arising as minimax decisions over confidence sets, or what Manski (2021) terms "as-if decisions with a set estimate." A parallel argument applies to E-certified decisions obtained from e-values in settings with unbounded loss.