Is this good for educators?

Yes — this version of "Bayesian Workbench for a click-through rate" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.

Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Educators · Bayesian Workbench

Bayesian Workbench for a click-through rate

Built for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs. Simulate a click-through rate live below — adjust the inputs and watch it respond, right in your browser.

Bayes Inference

open full solver →

Bayesian InferenceLive

prior × likelihood → posterior

Controls

Presets

Prior α (pseudo-heads)

Prior β (pseudo-tails)

Observed heads

Observed tails

Bayesian inference updates a prior belief with data to form a posterior. For a coin, a Beta prior combined with binomial coin flips gives a Beta posterior — the conjugate update is just adding heads to α and tails to β. Watch the posterior sharpen and shift as evidence accumulates.

▶ Run in Python

Data Inspector

Posterior mean0.667

Posterior SD0.094

Posterior α, β16.0, 8.0

Governing equation

p ∣ data \sim Beta (α + h, β + t) = Beta (16.0, 8.0), E [p] = \frac{α + h}{α + β + n} = 0.667

Reading this result: The posterior mean 0.667 sits between the prior mean 0.500 and the observed rate 0.700; with 20 flips versus 4.0 pseudo-counts, the data dominates and pulls the estimate toward the evidence.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

Monte Carlo

open full solver →

Monte Carlo Price SimulationLive

geometric Brownian motion

Controls

Presets

Initial price S₀

Expected return μ

Volatility σ

Horizon (years)

Geometric Brownian motion models a price with constant drift and random volatility — the assumption behind Black-Scholes. Running hundreds of simulated paths reveals the full distribution of outcomes, not just an average. Educational tool, not investment advice.

▶ Run in Python

Data Inspector

Median outcome$0

5th percentile$0

95th percentile$0

Governing equation

S_{t + Δ t} = S_{t} e^{(0.07 - \frac{0. 2 ^{2}}{2}) Δ t + 0.2 Δ t Z}, \tilde{S}_{1} \approx $0

Reading this result: Median outcome is about $0, just under the drift-only $107 — GBM compounds in log-space, so volatility always pulls the typical path below the average.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

Bootstrap

open full solver →

Bootstrap ResamplingLive

confidence without formulas

Controls

Presets

Original sample size

Bootstrap resamples B

The bootstrap estimates uncertainty by resampling your data with replacement thousands of times and recomputing the statistic each time. The spread of those bootstrap means gives a confidence interval — no formula or normality assumption required. Powerful when the math is intractable.

▶ Run in Python

Data Inspector

Sample mean0.00

95% CI low0.00

95% CI high0.00

CI width0.00

Governing equation

\hat{θ}^{*} = \frac{1}{25} i = 1 \sum 25 x_{i}^{*}, CI_{95%} = [\hat{θ}_{(2.5%)}^{*}, \hat{θ}_{(97.5%)}^{*}] = [0.00, 0.00]

Reading this result: The spread of the resampled means is the confidence interval — no normality assumption needed. Sample size sets its width; more resamples only sharpen its edges.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Students Researchers Engineers Hobbyists & Makers K-12 Students First Responders General version →

More with Bayesian Workbench

Bayesian Workbench for an A/B test Bayesian Workbench for a survey sample Bayesian Workbench for a poll margin Bayesian Workbench for a quality-control chart Bayesian Workbench for a clinical trial Bayesian Workbench for a customer churn Bayesian Workbench for an exam-score curve Bayesian Workbench for a defect rate

Frequently asked questions

Is this good for educators?: Yes — this version of "Bayesian Workbench for a click-through rate" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.