Bayesian Power Analysis (Assurance)
Bayesian Power Analysis (Assurance / Bayesian Sample Size Determination) · Also known as: assurance, bayesian sample size determination, bayesian assurance, Bayesian Güç Analizi (Assurance / Bayesian Sample Size)
Bayesian power analysis — also called assurance — is a sample size determination method that replaces the frequentist notion of power with a probability-weighted average over a prior distribution on the effect size. First formalised by Spiegelhalter and Freedman (1986) and further developed by O'Hagan, Stevens and Campbell (2005), it answers the question: given our current uncertainty about the true effect, what sample size gives us a high overall probability of obtaining a statistically significant result?
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use Bayesian power analysis when you can articulate a credible prior distribution over the effect size — for example from a pilot study, a systematic review, or expert elicitation — and you want your sample size justification to reflect parameter uncertainty honestly. It is especially appropriate in clinical trials, where the design prior and the analysis prior may deliberately differ: the design prior is broad and encodes genuine uncertainty, while the analysis prior may be skeptical or non-informative. The method accommodates continuous and binary outcomes. Require at least n = 10 per group; with smaller samples the simulation variance dominates and results are unreliable — use simulation-based power analysis instead.
Strengths & limitations
- Explicitly quantifies uncertainty about the effect size rather than conditioning on a single assumed value.
- Produces an assurance figure that is honest and generally more conservative than frequentist power, reducing underpowered studies.
- Allows the design prior and the analysis prior to differ, separating planning beliefs from inference beliefs.
- Naturally incorporates external evidence (pilot data, meta-analytic estimates) into sample size planning.
- Requires specification of a prior distribution; the assurance result depends on the prior, and a poorly chosen prior produces misleading sample sizes.
- No closed-form analytical formula in most cases — computation relies on Monte Carlo simulation, which introduces sampling variability.
- More conceptually demanding than frequentist power analysis; reviewers and ethics committees may be unfamiliar with the assurance framework.
- Does not eliminate the need for a minimum meaningful effect size; the prior must still be anchored to substantive knowledge.
Frequently asked
How is assurance different from frequentist power?
Frequentist power is computed at a single fixed assumed effect size. Assurance is an expectation of power over a prior distribution on the effect size. When the prior is a point mass at the assumed value, assurance equals frequentist power exactly. In all other cases, assurance is lower — because it averages over the full range of plausible effects, including smaller ones — and therefore provides a more realistic view of the probability of study success.
What prior should I use for the effect size?
The design prior should capture your genuine uncertainty before the study. Common choices are a Normal prior centred on the clinically meaningful effect with a standard deviation derived from a pilot study or meta-analysis, or a Student-t prior with heavier tails to express more uncertainty. It is good practice to run sensitivity analyses under several priors to confirm that the recommended sample size is robust.
Can I use different priors for design and analysis?
Yes — and this is one of the method's key features. The design prior is used only for sample size planning and can be broad and realistic. The analysis prior governs inference after data collection and is often sceptical or non-informative for regulatory contexts. Keeping the two separate prevents the planning assumptions from influencing the final inference.
Why can the result differ substantially from conventional power calculations?
Conventional power calculations are typically done at an optimistic effect size (often the minimum clinically important difference), which tends to be at the upper tail of what is realistically plausible. Because assurance averages across all prior-plausible effects — most of which are smaller — the assurance at the same n is lower. This difference is a feature, not a flaw: it reveals that conventional calculations may systematically underestimate the required sample size.
Sources
- O'Hagan, A., Stevens, J.W. & Campbell, M.J. (2005). Assurance in Clinical Trial Design. Pharmaceutical Statistics, 4(3), 187–201. DOI: 10.1002/pst.175 ↗
- Spiegelhalter, D.J. & Freedman, L.S. (1986). A Predictive Approach to Selecting the Size of a Clinical Trial, Based on Subjective Clinical Opinion. Statistics in Medicine, 5(1), 1–13. DOI: 10.1002/sim.4780050103 ↗
How to cite this page
ScholarGate. (2026, June 1). Bayesian Power Analysis (Assurance / Bayesian Sample Size Determination). ScholarGate. https://scholargate.app/en/statistics/bayesian-power-analysis
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 t-TestBayesian↔ compare
- Sequential AnalysisStatistics↔ compare
- Simulation-Based Power AnalysisStatistics↔ compare