Turn complex evidence into clearer decisions
Government agencies and foundations invest in evaluations to answer practical questions: Did a program work? How much did it help? What should leaders scale, target, redesign, or study further?
Those decisions get harder when findings are mixed, sample sizes are small, or new results need to be interpreted alongside earlier studies. Traditional methods remain essential, but decisions often require more than a statistically significant (or not) result. Bayesian methods add context: the probability that a program produced meaningful benefit, the likely size of that benefit, and whether the evidence is strong enough to act.
Mathematica applies Bayesian methods alongside traditional impact estimates or on their own when they are a better fit for the research question or available data, giving leaders clearer evidence to inform and decisions.
Bayesian methods can help you understand whether a program, policy, or intervention made a real difference, or whether the results were simply due to chance.
Talk to an expertUse Bayesian methods when uncertainty could delay action
Bayesian methods are especially useful when leaders need to interpret:
Many outcomes or subgroup results
Small samples for priority populations, geographies, or providers
Large administrative data sets with complex structures
New findings that build on prior research
In these settings, decision makers need more than a binary threshold, such as whether results are or are not statistically significant. They need to know the likelihood of meaningful improvement and whether the evidence supports scaling, targeting, redesigning, or further study.
Match Bayesian support to your decision
Mathematica helps clients apply Bayesian methods when they can help improve decisions. We tailor our approach to the question, data, study design, timeline, and decision at stake, and transparently incorporate prior evidence established through systematic reviews, meta-analyses, curated evidence bases, and sensitivity testing.
Interpret one evaluation in context with BASIE
BASIE (Bayesian Interpretation of Estimates) combines prior evidence with new findings to produce a probability-based, policy-relevant interpretation. It helps decision makers judge whether an evaluation supports scale-up, redesign, further study, or no change.
Explore the BASIE Framework, developed by Mathematica for the U.S. Department of Education.
Improve subgroup insight in large and complex data sets
For evaluations with millions of records, clustered designs, or large administrative data sets, important differences across subgroups can be difficult to interpret with confidence. Bayesian methods stabilize subgroup estimates and help leaders see where results are most likely to differ across groups of people, places, or time periods.
Mathematica used a hybrid Bayesian method to evaluate the Centers for Medicare & Medicaid Services Primary Care First Model, finding that it did not meaningfully reduce hospitalizations and likely increased costs—evidence leaders could use to assess model performance, payment design, and future evaluation needs.
Combine evidence across studies to guide next investments
Bayesian meta-analysis and evidence synthesis help leaders weigh prior evidence alongside new results to inform evaluation design, policy updates, systematic reviews, and portfolio decisions.
Mathematica synthesized evidence from more than 8,000+ studies on 221 interventions to identify which workforce services are most likely to improve outcomes.
Build a custom Bayesian approach for high-stakes decisions
For technically complex studies, Mathematica designs tailored Bayesian analyses when standard approaches cannot fully answer the question. Bayesian approaches can handle multi-level data structures, correlated outcomes, adaptive designs, and sequential decisions within one framework. Use custom Bayesian modeling when a scale-up, funding, or program-design decision depends on evidence that standard analyses cannot summarize well enough.
Mathematica developed a person-level Bayesian model to estimate the effect of the Medicare Care Choices Model on a range of outcomes overall and among key subgroups, giving decision makers a clearer view of where the model showed promise and where results were uncertain.
Identify where Bayesian methods can improve decision making
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