Bayesian Statistics & Probabilistic Programming Certification

The Bayesian Statistics & Probabilistic Programming Certification is a free advanced-level, 25-minute skill test from Science of Apps. It tests Bayesian statistics and probabilistic programming — Bayes' theorem, priors, likelihoods and posteriors, conjugate models such as beta-binomial, choosing weakly informative priors, posterior summaries and credible intervals, Markov chain Monte Carlo, Hamiltonian Monte Carlo and NUTS, convergence diagnostics such as R-hat and effective sample size, hierarchical and multilevel models with partial pooling, posterior predictive checks, model comparison with LOO and WAIC, Bayesian A/B testing and decision analysis, variational inference, and workflows in Stan and PyMC — written to Gelman et al.'s Bayesian Data Analysis, the Stan User's Guide and PyMC documentation for 2026 and 2027. Score 70% or more on its 25 questions to earn a verifiable Bayesian Statistics & Probabilistic Programming certificate (SOA-BSPP). Every question is based on published standards and research — including Bayesian Data Analysis, third edition (free PDF) (Andrew Gelman et al.), Stan User's Guide (Stan Development Team), PyMC documentation and examples (PyMC developers) — and each answer is explained with its source.

Science of Apps offers a free Bayesian Statistics & Probabilistic Programming Certification, written for 2026 and 2027. It tests Bayesian foundations, computation, hierarchical modelling, model checking and comparison and applications and tools with 25 original scenario questions in all, each naming its published source; you get an instant score and a verifiable certificate with a credential ID you can add to LinkedIn.

Read the five skill areas on this page, then take the 25-minute test online — no fee, course or sign-up. You see every answer explained when you finish. Score 70% or more and you get a Bayesian Statistics & Probabilistic Programming certificate straight away, on screen, as a PDF and by email, with a credential ID anyone can verify.

Yes. The questions are original scenarios written by Science of Apps, and each one is based on a public source you can read: Bayesian Data Analysis, third edition (free PDF) (Andrew Gelman et al.); Stan User's Guide (Stan Development Team); PyMC documentation and examples (PyMC developers). The source is shown under each question and linked in the answer review. Science of Apps doesn't copy questions from other tests.

Five skill areas with five questions each, drawn from a bank of 10 per area so a retake brings new questions: Bayesian Foundations (Bayes' theorem, Priors and likelihoods and Posterior summaries); Computation (MCMC, Hamiltonian Monte Carlo and Diagnostics); Hierarchical Modelling (Pooling, Multilevel structure and Group-level priors); Model Checking and Comparison (Posterior predictive checks, Model comparison and Robustness); Applications and Tools (Bayesian A/B testing, Decision analysis and Software and VI). Every question is an original scenario written to the 2026–2027 standard, with the published source named under it.

Data scientist or statistician, Quantitative researcher or analyst, Experimentation or product analytics lead, Scientist modelling uncertainty and Machine learning engineer working with probabilistic models. It suits students at leading universities, career switchers and experienced professionals who want quick, verifiable proof of Bayesian Statistics & Probabilistic Programming knowledge in 2026 and 2027.

CS and AI students at MIT, Stanford, CMU, Berkeley, IITs, Tsinghua and ETH are hired on depth beyond tool use: model internals, systems and hardware. Passing earns a founder-signed Science of Apps certificate with a credential ID and QR code that recruiters can verify.

A 95% credible interval contains the parameter with 95% posterior probability given the model and data. A frequentist 95% confidence interval is a procedure that would cover the true value in 95% of repeated samples.

R-hat compares variation within and between MCMC chains. Values close to 1 (for example below 1.01) suggest the chains have mixed and converged; larger values indicate problems.

Yes. The test is online, in English and free everywhere — people take it from India, the US, the UK, Europe, Africa, Latin America and Asia-Pacific. Your certificate is dated with your own local date and can be verified from anywhere at scienceofapps.com/certification/verify/.

25 questions — 5 from each of 5 skill areas — with a 25-minute limit. You need 70% (18 of 25) to pass and 90% for distinction.

We rate it Advanced: assumes years in the role or deep specialist knowledge. It has 25 scenario questions — 5 from each of 5 skill areas — and a 25-minute limit. You need 70% (18 of 25) to pass and 90% for distinction.

Nothing. There is no fee to take a test, to receive the certificate, to have it emailed or to verify it, and no sign-up.

On our server, not in your browser. The answers never reach the page until you submit, so a certificate can only be earned by passing. Each certificate gets a unique credential ID stored by Science of Apps.

You see your score for each area and every question with the correct answer and why, with the published source behind it. You can retake after 30 minutes, and the retake draws questions you haven't seen yet.

No. Every certificate is dated, so it always shows when you passed. Retake a test any time for a newer date or a higher score.

Yes. After you pass, Add to LinkedIn opens the Licenses & certifications form with the certificate name, Science of Apps as the issuer, the issue date, your credential ID and the verification link filled in. You can also download it as a PDF or PNG, and it's emailed to you as a PDF.

Every certificate has a credential ID and a QR code. Scanning it, or entering the ID at scienceofapps.com/certification/verify/, shows the holder's name, the certification, the score and the issue date from our records.

No. They are Science of Apps' own assessments of applied skill. They aren't issued by a university or standards body, and they work best alongside a portfolio that shows the skills in real work.