Bayesian Counterfactual Impact Evaluation
Also known as: Bayesian CIE, Bayesian causal impact, Bayesian structural time-series causal inference, BSTS counterfactual evaluation
Bayesian Counterfactual Impact Evaluation estimates the causal effect of an intervention by constructing a Bayesian posterior distribution over the counterfactual outcome — what would have happened without treatment. The method, popularized by Brodersen et al. (2015) through the CausalImpact framework, uses Bayesian structural time-series models fitted on the pre-intervention period to predict the counterfactual trajectory, then compares observed post-intervention outcomes to that prediction.
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When to use it
Use Bayesian counterfactual impact evaluation when you have a single treated unit (or a small number of treated units) with a long pre-intervention time series and access to control time series that track the treated unit before the intervention. It is ideal for evaluating the impact of a one-time policy, marketing campaign, product launch, or regulatory change on a measured outcome over time. Do not use it when the pre-intervention period is too short (fewer than ~20 time points) to reliably estimate the counterfactual model, when no credible control series exist, when treatment is continuous rather than a sharp event, or when outcomes are discrete counts with very small rates where BSTS Gaussian assumptions break down.
Strengths & limitations
- Provides full posterior uncertainty quantification over the causal effect, not just a point estimate and frequentist p-value.
- Handles complex time-series structure (trend, seasonality, structural breaks) through the BSTS framework.
- Automatic variable selection via spike-and-slab priors guards against overfitting when many control series are available.
- Can evaluate dynamic causal effects at each post-intervention time point, not only a single average effect.
- Applicable to a single treated unit, where methods requiring many treated units (e.g., standard DiD) are infeasible.
- Requires a sufficiently long pre-intervention series (at least 20 time points, ideally 50+) to identify time-series dynamics reliably.
- The counterfactual is only as valid as the control series — if controls are also affected by the intervention (spillovers), the estimate is biased.
- Computationally more demanding than frequentist alternatives; MCMC-based inference can be slow for very long series.
- Assumes the relationship between the outcome and control covariates is stable across the pre- and post-intervention periods.
- Sensitivity to prior specification can be material in small samples; poorly chosen priors may dominate the posterior.
Frequently asked
What is the key difference between Bayesian counterfactual impact evaluation and standard interrupted time series?
Standard interrupted time-series uses frequentist regression with a level/slope change at the intervention point. The Bayesian approach additionally models latent state dynamics, incorporates control covariates for the counterfactual, and produces a full posterior distribution over the effect rather than a point estimate with standard errors.
How many pre-intervention time points do I need?
A practical minimum is around 20 time points pre-intervention, but reliable estimation of trend and seasonality typically requires 50 or more. The longer the pre-intervention window, the more credible the counterfactual forecast.
What if I have no control time series?
The method can still be applied using a trend-plus-seasonality BSTS model without covariates, but the counterfactual will be noisier and rely heavily on extrapolating pre-intervention dynamics. Credible controls substantially improve precision.
How do I interpret the posterior probability of a causal effect?
The posterior probability that the effect is positive (or larger than some threshold) is a direct probability statement under the model — for instance, 'there is a 97% posterior probability that the cumulative effect is positive.' This is more interpretable than a frequentist p-value but is still model-dependent.
Can I use this method for multiple treated units?
Yes, but each unit typically receives its own BSTS model and its own counterfactual. Aggregating effects across units requires additional pooling assumptions. For many treated units with panel data, difference-in-differences or synthetic control methods may be more appropriate.
Sources
- Brodersen, K. H., Gallusser, F., Koehler, J., Remy, N., & Scott, S. L. (2015). Inferring causal impact using Bayesian structural time-series models. Annals of Applied Statistics, 9(1), 247-274. DOI: 10.1214/14-AOAS788 ↗
- Rubin, D. B. (2005). Causal inference using potential outcomes: Design, modeling, decisions. Journal of the American Statistical Association, 100(469), 322-331. DOI: 10.1198/016214504000001880 ↗
How to cite this page
ScholarGate. (2026, June 3). Bayesian Counterfactual Impact Evaluation. ScholarGate. https://scholargate.app/en/causal-inference/bayesian-counterfactual-impact-evaluation
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Bayesian Difference-in-DifferencesCausal inference↔ compare
- Causal Impact AnalysisCausal inference↔ compare
- Counterfactual Impact EvaluationCausal inference↔ compare
- Difference-in-DifferencesEconometrics↔ compare
- Synthetic Control MethodCausal inference↔ compare