What is the Bayesian Workbench multi-solver?

Bayesian Workbench is a guided workflow that chains 3 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.

Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.

Data & Statistics Pack · Multi-Solver

Bayesian Workbench

Prior to posterior. This multi-solver chains 3 solvers into a single guided workflow — run each step in order and carry the result forward.

Workflow steps

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Bayes Inference

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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.

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Monte Carlo

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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.

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Bootstrap

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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.

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More in the Data & Statistics pack

ML Model Trainer Classification Pipeline Clustering Workbench Feature Engineering Deep Net Playground Recommender System Anomaly Detection Time-Series Forecaster

Frequently asked questions

What is the Bayesian Workbench multi-solver?: Bayesian Workbench is a guided workflow that chains 3 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.
Is it free to use?: Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.