Continuous Probability & Bayesian Learning

The Mystery of the Two Peaks. Early summer, and something has changed: this semester’s bentos arrive wrapped in furoshiki — opaque. Chibany, refusing to peek, starts weighing them, and the weights refuse to behave: the average is 441 g, yet no bento ever weighs 441 g. Solving that mystery takes this whole Part: continuous quantities need densities instead of counts, bumps need Gaussians, learning needs priors that become posteriors, and the two peaks themselves need mixture models.

graph LR
    A[Mystery<br>Bentos] --> B[Continuous<br>Probability]
    B --> C[The<br>Gaussian]
    C --> D[Bayesian<br>Learning]
    D --> E[Mixture<br>Models]

    style B fill:#27ae60,color:#fff
    style D fill:#27ae60,color:#fff

Everything runs on the GenJAX you learned in The Tools — probabilities become densities, sums become integrals, counting becomes area, but the code barely changes. No calculus required: intuition first, visuals and code before math.

Chapters

• Chibany's Mystery Bentos
• The Continuum: Continuous Probability
• The Gaussian Distribution
• Bayesian Learning with Gaussians
• Gaussian Mixture Models

Wondering how many kinds of bento there really are, or whether a model can be too flexible? That thread continues in How Complex Should a Model Be? — best read after Decisions & RL.

This project is generously funded by the Japanese Probabilistic Computing Consortium Association (JPCCA).