Bayes Thinking Lab v0.9 beta

Statistical Intuition, Reimagined.

🌐 www.bayes-thinking-lab.uni-osnabrueck.de

20 interactive tools that guide users from frequentist foundations through Bayesian multi-level modeling to principled posterior decision-making — including causal effect estimation via G-Computation, DAG-based causal reasoning, parametric data generation, and GLM-scale prior specification.

[ Learning Path ] • [ Ecosystem ] • [ Philosophy ] • [ Usage ] • [ GitHub Repository ]

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🔭 Scientific Philosophy

The Bayes Thinking Lab (BTL) moves away from the "black-box" approach of statistical software. Inspired by the pedagogical works of John Kruschke and Richard McElreath, this project emphasizes:

• Visual Proofs: Concepts like Partial Pooling, Link Functions, and HDI vs. ROPE become tangible through real-time manipulation.
• The Formula-Graphic Duality: Hierarchical models are simultaneously represented as Kruschke-style diagrams and in mathematical notation consistent with McElreath and brms.
• Workflow Integration: Beyond interactive demos, the lab functions as a productivity tool — generating production-ready brms code for R and supporting the full Bayesian workflow from prior specification to posterior decision.

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🗺 The Learning Path

The lab is organized into five sections that build on each other. Work through them in order, or jump in wherever your current knowledge begins.

Section	What you will learn	Key Tools
0 · Foundations	Why the GLM is the gateway to Bayesian thinking	Interactive LM · MLE Tool · LM→GLM Transition
I · GLM & GLMM	How regression generalizes across distributions and hierarchies	GLM Conditional Distributions · GLM 3D · Interactive GLMM
II · Bayesian Intuition	How to think in probability distributions and update beliefs from data	Thinking Simulator · Prior Lab · MCMC Visualizer · Bayes Interactive
III · Small Worlds	How to construct models: sketch causal structure, simulate data, plan power	Golem Builder · Data Creator
IV · Bayesian Workflow	How to specify, build, check, compare, and export hierarchical Bayesian models	Model Architect · brms Builder · Prior & Posterior PPC · LOO Lab
V · Posterior Decision	How to make principled, transparent decisions from posterior distributions	Causal Calculator · Decision Lab · Decision Maker

⬡ Workflow tip: Use the Golem Builder (Section III — Small Worlds) to do the causal groundwork: draw your DAG, identify confounders, and determine the correct adjustment set. The Causal Calculator (Section V) then shows — with a worked example — how to implement exactly this kind of analysis via G-Computation in brms.

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🛠 The Ecosystem

0. Statistical Foundations

Master the GLM — the prerequisite for Bayesian thinking.

• Interactive LM — Manipulate data points and watch OLS minimization and residuals update in real time. Build intuition for what a regression line actually optimizes.
• Maximum Likelihood — Explore the conceptual distinction between probability and likelihood by adjusting parameters interactively against simulated data.

• LM → GLM Transition — Discover why link functions are necessary for non-normal outcomes and how the GLM generalizes the linear model across distribution families.

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I. From LM to GLMM

Scale the hierarchy of linear modeling.

• GLM Conditional Distributions — Visualize the conditional distribution y|x along a predictor across 8 model families: Normal, Student-t, Bernoulli (logistic), Poisson, Gamma, Ordinal (cumulative logit), Zero-Inflated Poisson, and Hurdle-Poisson. Compare parameter behavior and link functions across families.
• GLM in 3D — Interact with regression planes and residuals in a spatial environment. Explore how multiple predictors jointly determine the outcome surface.
• Interactive GLMM — Simulate grouped data and compare Complete Pooling, No Pooling, and Partial Pooling side by side. Observe Simpson's Paradox, the Intraclass Correlation Coefficient (ICC), and the shrinkage mechanism — for Normal, Poisson, Gamma, and logistic outcomes.

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II. Bayesian Intuition

Learn to think in probability distributions.

• Bayesian Thinking Simulator — Work through 8 psychological scenarios that build qualitative updating intuition without requiring mathematical notation.
• Prior Lab — Translate verbal uncertainty statements into mathematical priors across 12 distributions. A real-time CI-solver maps your beliefs onto distribution parameters. GLM Mode (new in v1.0): enter your bounds as probabilities (logit-link) or expected values (log-link) — the solver converts to model scale automatically, and a dual-panel plot shows both the prior as brms needs it and what it implies on the response scale (probabilities, Odds Ratios, Rate Ratios) — via a mathematically exact Jacobian transformation (change-of-variables theorem), not an approximation.

• MCMC Visualizer — Watch the Metropolis-Hastings sampler navigate the posterior landscape — the "animated hiker" analogy made interactive.

* **Bayes Interactive** — Manipulate prior strength, likelihood, and sample size and see how they jointly shape the posterior. Includes CI and PPI bands for the full posterior predictive.

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III. Small Worlds

Named after Richard McElreath (Statistical Rethinking, Ch. 2): a model is a "small world" — a simplified, consistent representation of reality. Before real data are collected or models fitted, it is worth explicitly constructing and simulating this small world.

• Golem Builder — Draw directed acyclic graphs (DAGs), compute d-separation and testable implications (compatible with dagitty), identify minimal adjustment sets, detect instrumental variables and the Front Door criterion. Quantify relationships, simulate data directly from the DAG, and export production-ready brms and glmmTMB analysis code — all in the browser. Exactly following McElreath's approach.

• Data Creator — Parametric data generation for all common designs: between-subjects, within-subjects (repeated measures), and mixed designs — with covariates, cluster structures (random intercepts & slopes), and arbitrary sample sizes. Supports 10 likelihood families (Gaussian, Student-t, Log-Normal, Gamma, Bernoulli, Beta, Binomial, Poisson, Negative Binomial). Full faux and glmmTMB R code export, plus a commented simulation-based power analysis block (glmmTMB + car::Anova) — ready to run in R.

⬡ Workflow tip: Do the causal groundwork in the Golem Builder first — draw your DAG, identify which variables to adjust for and why. The Causal Calculator (Section V) then demonstrates how to implement exactly this analysis via G-Computation in brms.

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IV. Bayesian Workflow

Tools for the applied scientist.

• Bayesian Model Architect — Build hierarchical Bayesian model structures visually in Kruschke-diagram style. See how priors, hyperpriors, and random effects (intercepts and slopes: u₀ⱼ, u₁ⱼ, τ₀, τ₁) connect in a live diagram — then generate R simulation code for prior predictive checking.
• brms Model Builder — Specify complex hierarchical models step by step across 15+ likelihood families, polynomial terms, interactions, and distributional parameters. Export production-ready brms code for R. The generated code includes a commented-out posterior_predict() export block — ready to load into the Posterior Predictive Check app.
• Prior Predictive Check — Import your brms model specification, explore the prior predictive distribution, and validate that your priors generate plausible data before fitting.
• Posterior Predictive Check — Evaluate model fit and posterior behavior via a dedicated Shiny app (R/bayesplot). Upload a saved brms object (saveRDS(fit, "model.rds")), walk through KDE overlay, summary statistics, error structure, and prediction intervals with guided evaluation.
• LOO Lab — Compare models after fitting. Paste loo_compare() output directly from R and receive an annotated forest plot, Pareto-k diagnostics, and a traffic-light decision rule. Includes an animated LOO walkthrough (Stage 1) that requires no R.

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V. Posterior Decision

Move from estimation to decision.

• Causal Calculator — A worked example of causal effect estimation via G-Computation (standardization). Shows how to make confounding visible, correct naive regression bias, and compare ATE, ATT, and ATU — visualized as counterfactual distributions. Use the Golem Builder to identify the correct adjustment set for your own research question; the Causal Calculator shows how to implement that analysis in brms. Exports draws compatible with the Decision Maker.
• Decision Lab — Apply three principled decision frameworks to any posterior distribution: Kruschke's HDI vs. ROPE trichotomy (accept / reject / undecided), Full ROPE % (probability of practical equivalence), and ETI vs. ROPE. Supports Normal, Student-t, and Gamma posteriors with analytically correct HDI and ETI computation.
• Decision Maker — Upload your own posterior samples via CSV (from brms, Stan, or rstanarm), define transformations and derived quantities as formulas (Cohen's d, Odds Ratios, etc.), compute HDI and ETI, and export a complete APA-formatted decision report — ready to paste into a manuscript.

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🚀 Getting Started

The Bayes Thinking Lab is a serverless web application. No installation, no backend, and no data leaves your machine.

1. Clone the repository:

   git clone https://github.com/raduesing/Bayes_Thinking_Lab.git

2. Open index.html in any modern web browser.
3. Follow the learning path — or jump directly to the tool that matches your current need.

Tip: Each tool includes a built-in ℹ Help panel and inline explanations for every parameter. Use the Guide in Model Architect and brms Builder for step-by-step walkthroughs.

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🎓 Target Audience

Level	Recommended Entry Point	Tools to Explore
BSc Students	Section 0 — Foundations	Interactive LM · MLE Tool · Thinking Simulator · Prior Lab (CI-Solver) · Bayes Interactive
MSc Students	Section I–II	GLM Conditional Distributions · Interactive GLMM · Prior Lab (GLM Mode) · Model Architect · Decision Lab
PhD / Researchers	Section III–V	Golem Builder · Data Creator · brms Model Builder · Prior & Posterior PPC · LOO Lab · Causal Calculator · Decision Maker

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🛠 Built With

Vanilla JS · D3.js · No framework · No build step · Runs entirely in the browser.

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🖋 Scientific Acknowledgments

The development of the Bayes Thinking Lab is grounded in the pedagogical and methodological frameworks established by the following researchers:

Author	Framework / Contribution	Resource
John K. Kruschke	Graphical model representations follow the Kruschke Diagram conventions from Doing Bayesian Data Analysis.	Blog
Richard McElreath	Model notation, workflow structure, and prior predictive thinking are informed by Statistical Rethinking (Ch. 5–6, 14).	GitHub
A. Solomon Kurz	Acknowledgment to his brms and tidyverse translations of Kruschke and McElreath, which informed several implementation details.	Website
Paul-Christian Bürkner	All exported code targets the brms R package. Prior notation (class=sd, τ₀, τ₁) follows brms conventions.	brms

Note on Licensing: This project is released under the MIT License. All external references and conceptual frameworks belong to their respective copyright holders.

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🎓 Citation

If you use the Bayes Thinking Lab for research, teaching, or software development, please cite it as follows:

APA Style

Düsing, R. (2026). Bayes Thinking Lab: An interactive suite for Bayesian intuition and brms workflow (Version 0.9 beta). GitHub. https://github.com/raduesing/Bayes_Thinking_Lab

BibTeX

@software{Duesing_Bayes_Thinking_Lab_2026,
  author  = {Düsing, Rainer},
  title   = {{Bayes Thinking Lab: An interactive suite for Bayesian intuition and brms workflow}},
  url     = {https://github.com/raduesing/Bayes_Thinking_Lab},
  version = {0.9.0},
  year    = {2026}
}

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📬 Contact

Bayes Thinking Lab · University of Osnabrück
✉️ www-b-t-l@uni-osnabrueck.de