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LearnProbabilityMechanisms, distributions, transformations, and limits.Bayesian learningPosterior updates, Thompson sampling, and Bayesian optimization.Deep learningActivations, likelihood-derived objectives, and the architectures built from them.01Activations02Likelihood to loss03ObjectivesSemi-supervisedUse a few labels and many unlabeled examples without hiding the assumptions.ReferenceDistributionsRelationship mapSource & method

Beta

A flexible model for proportions and the conjugate prior for Bernoulli probability.
Type continuousSupport 0 < x < 1Family Bounded
Probability densityf(x) = xᵅ⁻¹(1−x)ᵝ⁻¹ / B(α,β)
continuous

Beta in motion

0.00.30.50.81.0
Support0 < x < 1
Mean0.2857
Variance0.02551
Connections

Where the beta
comes from — and leads.

Every link is one of the four moves from the relationship map: special cases, transformations, limits, and Bayesian conjugacy.

Bernoullip ~ Beta

Beta is conjugate to Bernoulli likelihood; posterior parameters add successes and failures.

BayesianBinomialp ~ Beta

Beta is conjugate to a binomial likelihood.

Bayesian

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See every connection at once.

The relationship map draws the whole backbone — special cases, transformations, limits, and conjugacies — in one guided view.

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