Primary Submission Category: Bayesian Causal Inference
Bay-PIE: Correcting Attenuation Bias in Predictive Incrementality by Experimentation
Authors: Ran Wang,
Presenting Author: Ran Wang*
Predictive Incrementality by Experimentation (PIE; Gordon et al., 2023) calibrates attribution by relating total lift to attributed lift across many randomized experiments. In practice, both lifts are often noisy finite-sample estimates with heterogeneous standard errors, and they may share sampling noise within an experiment. Conventional OLS/WLS PIE can therefore exhibit attenuation bias, inefficient weighting, and poorly calibrated intervals.
We propose Bayesian PIE (Bay-PIE), a Hierarchical Bayesian Model for the latent PIE relationship. Both observed lifts are treated as error-contaminated measurements (e.g., hat{tau}_i^{total}=tau_i^{total}+v_i^{total}, hat{tau}_i^{attr}=tau_i^{attr}+v_i^{attr}); Bay-PIE effectively deconvolves measurement noise to recover latent lifts, with within-experiment dependence reduced via sample splitting. In simulations, Bay-PIE reduces bias and improves interval coverage versus WLS PIE, with larger gains when attribution is noisier. Using the public Criteo Attribution Modeling for Bidding dataset, Bay-PIE corrects slope shrinkage and helps separate low-signal from low-precision regimes. The key advantage is modularity for predictive-incrementality calibration: Bay-PIE casts PIE as a single probabilistic measurement-error model where weighting and extensions are built into the Bayesian framework and estimated via unified MCMC posterior inference, rather than using ad-hoc weighting rules or re-derived OLS/MLE estimators.