# Slamming the sham: A Bayesian model for adaptive adjustment with noisy control data

## TL;DR

This paper introduces a Bayesian hierarchical model for adaptive adjustment in causal inference, improving statistical efficiency by optimally balancing bias and variance in repeated experiments.

## Contribution

It presents a novel Bayesian approach that adaptively determines the amount of control data adjustment, enhancing analysis efficiency over traditional methods.

## Key findings

- Increased statistical efficiency in real and simulated data
- Improved experimental conclusions due to adaptive adjustment
- Demonstrated relevance to causal inference and experimental design

## Abstract

It is not always clear how to adjust for control data in causal inference, balancing the goals of reducing bias and variance. We show how, in a setting with repeated experiments, Bayesian hierarchical modeling yields an adaptive procedure that uses the data to determine how much adjustment to perform. The result is a novel analysis with increased statistical efficiency compared to the default analysis based on difference estimates. We demonstrate this procedure on two real examples, as well as on a series of simulated datasets. We show that the increased efficiency can have real-world consequences in terms of the conclusions that can be drawn from the experiments. We also discuss the relevance of this work to causal inference and statistical design and analysis more generally.