Statistics
π(θ) Bayesian Statistics
Treating unknowns as probability distributions and updating beliefs with data — from Bayes' theorem through modern computational methods.
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Bayes' Theorem
The rule for updating a belief in light of new evidence — turning P(evidence | hypothesis) into the far more useful P(hypothesis | evidence).
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Bayesian Inference
Treating unknown parameters as random variables with a prior distribution, then updating to a posterior as data arrives — the alternative to frequentist confidence intervals and p-values.
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Markov Chain Monte Carlo
Sampling from a posterior distribution you can't write down in closed form, by building a random walk whose long-run behavior matches that distribution.
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INLA
Integrated Nested Laplace Approximation — a fast, deterministic alternative to MCMC for a broad class of Bayesian models, trading some generality for speed and reliable convergence.
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Naive Bayes
A probabilistic classifier that applies Bayes' theorem with the (often unrealistic) assumption that features are conditionally independent given the class.