Prediction can be safely used as a proxy for explanation in causally consistent Bayesian generalized linear models

TL;DR

This paper investigates when prediction can reliably serve as a proxy for explanation in Bayesian generalized linear models, emphasizing the importance of causal consistency for valid model selection.

Contribution

It provides a systematic analysis through large-scale simulations to determine the conditions under which prediction accurately reflects causal explanations in Bayesian models.

Findings

Prediction is a valid proxy for explanation only under causal consistency.

Model misspecification leads to unreliable explanations based on predictions.

Ensuring models align with the causal structure is crucial for trustworthy inference.

Abstract

Bayesian modeling provides a principled approach to quantifying uncertainty in model parameters and model structure and has seen a surge of applications in recent years. Within the context of a Bayesian workflow, we are concerned with model selection for the purpose of finding models that best explain the data, that is, help us understand the underlying data generating process. Since we rarely have access to the true process, all we are left with during real-world analyses is incomplete causal knowledge from sources outside of the current data and model predictions of said data. This leads to the important question of when the use of prediction as a proxy for explanation for the purpose of model selection is valid. We approach this question by means of large-scale simulations of Bayesian generalized linear models where we investigate various causal and statistical misspecifications. Our results indicate that the use of prediction as proxy for explanation is valid and safe only when the models under consideration are sufficiently consistent with the underlying causal structure of the true data generating process.