PEOPLE ANALYTICS · AN INTERACTIVE EXPLORATION
Bayes in
your browser.
A question. A little data.
A clearer view of uncertainty.
Explore attrition, income and ordered ratings in a fictional workforce. Choose a model, watch it sample, and see a range of plausible answers—all on your own device.
Try an analysisNo account. No server-side model. No data leaves this app.
THE BAYESIAN IDEA
Update what you believe
with what you observe.
- 01
Start with a prior
Make assumptions explicit before using the data.
- 02
Bring in the evidence
The likelihood describes how the model could generate the observations.
- 03
Explore the posterior
Retained draws show which parameter values remain plausible.
Sampling gives us a practical way to explore posteriors, including ones without a simple closed form.
Small data still has uncertainty.
Priors can stabilize small-sample estimates, while keeping assumptions open to scrutiny.
Keep the whole range.
A credible interval is more informative than treating one estimate as the answer.
Watch the work happen.
Four seeded streams run locally. Logistic, ordinal and hierarchical models use live MCMC in a browser worker.
THE BROWSER LAB
What would you like to explore?
Loading the data
The bundled fictional workforce stays in this browser.
YOUR RESULTS WILL APPEAR HERE
Let the uncertainty
be part of the answer.
Choose your scope and settings, then sample the posterior. You’ll see plausible values, 50% and 95% credible intervals, and a trace of the draws that produced them.
POSTERIOR RESULTS
Histogram of all retained draws. Darker bins are centred inside the 95% credible interval; lighter bins are the tails. The dashed line marks the posterior median.
Retained iteration is on the horizontal axis. A drawing of the trace is downsampled for display; all retained draws enter the summaries and diagnostics.
Posterior summary & diagnostics
| Parameter / unit | Median | 50% interval | 95% interval | P(> reference) | Split R-hat | ESS ≈ |
|---|
Slope coefficients and group deviations use reference 0; multipliers use reference 1. Absolute locations, thresholds, log gaps and variance shares have no directional reference. A dash means no reference is defined. Table probabilities are model-conditional, not p-values. Displayed results use two decimal places; calculations and JSON exports retain full numerical precision. Warning thresholds use unrounded diagnostics, so rounding can mask a boundary (for example, R-hat may display 1.01 and still be flagged).
How to read the checks
We flag classical split R-hat above 1.01 and approximate effective sample size (ESS) below 400. Undefined, nonfinite or frozen streams also trigger warnings. These are practical checks, not proof of convergence or model adequacy. No posterior predictive check or test of proportional odds is implemented. Common residual variance and exchangeable group deviations are model assumptions, not conclusions from these checks. This R-hat is not rank-normalized; ESS uses an initial-positive-pair autocorrelation estimate.
Exact conjugate draws are independent by construction; their diagnostics provide an additional implementation check. Logistic and ordinal MALA adapt their step sizes only during discarded warmup. Hierarchical blocked Gibbs discards warmup sweeps and requires no proposal tuning. All four streams have different deterministic seeds.
Income comparison and ordinary income regression use Normal–Inverse-Gamma priors; their exponentiated coefficients have no finite posterior means. Hierarchical income uses different independent priors and reports natural income medians by presentation choice. Intervals concern model parameters, not individual employees’ future outcomes.
A DEMONSTRATION, WITH CONTEXT
A familiar dataset.
A fictional workforce.
The IBM HR Analytics Employee Attrition & Performance dataset contains 1,470 fictional employees and 237 Attrition = Yes records. IBM data scientists created it for demonstration. It is not a sample of actual IBM employees.
There is no documented attrition observation window, so these proportions are not annual turnover rates. Monthly income is in unspecified income units/month. No currency is assumed.
Try a smaller department to see how the prior and sample size affect uncertainty. The models describe associations in this dataset; they do not establish causes or provide a validated operational prediction system.
Original dataset on Kaggle ↗ · Download the original CSV · Source & license details
Data: Open Database License 1.0 and Database Contents License 1.0. Numeric strings are parsed for the app; no values are imputed or fabricated.
GO A LITTLE DEEPER
Inspired by Bayesian Thinking
for People Analytics.
These are independent adaptations using the IBM demonstration data. Andrew Marritt’s book uses brms, Stan and HMC; this app uses exact conjugate sampling, MALA for logistic and ordinal regression, and blocked Gibbs for hierarchical income. The implementations are different.