Incentive-Theoretic Bayesian Inference for Collaborative Science

TL;DR

This paper develops a Bayesian inference framework for collaborative science that accounts for strategic agent behavior, enabling principals to infer private priors and improve decision-making in scientific trials.

Contribution

It introduces a novel incentive-theoretic approach to hypothesis testing that leverages agents' strategic trial choices to infer private information and optimize inference policies.

Findings

Principal can design policies to extract partial information from agents' trial decisions.

Guidelines for setting significance thresholds based on trial costs and firm profits.

The approach improves inference accuracy in strategic, collaborative research environments.

Abstract

Contemporary scientific research is a distributed, collaborative endeavor, carried out by teams of researchers, regulatory institutions, funding agencies, commercial partners, and scientific bodies, all interacting with each other and facing different incentives. To maintain scientific rigor, statistical methods should acknowledge this state of affairs. To this end, we study hypothesis testing when there is an agent (e.g., a researcher or a pharmaceutical company) with a private prior about an unknown parameter and a principal (e.g., a policymaker or regulator) who wishes to make decisions based on the parameter value. The agent chooses whether to run a statistical trial based on their private prior and then the result of the trial is used by the principal to reach a decision. We show how the principal can conduct statistical inference that leverages the information that is revealed by an agent's strategic behavior -- their choice to run a trial or not. In particular, we show how the principal can design a policy to elucidate partial information about the agent's private prior beliefs and use this to control the posterior probability of the null. One implication is a simple guideline for the choice of significance threshold in clinical trials: the type-I error level should be set to be strictly less than the cost of the trial divided by the firm's profit if the trial is successful.