Editing Bayesian Ml (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Prior distribution''' — A probability distribution over model parameters encoding beliefs before seeing any data; P(θ).
* '''Likelihood''' — The probability of observing the data given model parameters; P(D|θ).
* '''Posterior distribution''' — Updated beliefs about parameters after observing data; P(θ|D) ∝ P(D|θ)P(θ).
* '''Bayes' theorem''' — P(θ|D) = P(D|θ)P(θ) / P(D); the foundation of Bayesian inference.
* '''Marginal likelihood (evidence)''' — P(D) = ∫ P(D|θ)P(θ)dθ; normalizing constant; used for model selection.
* '''Posterior predictive''' — Predictions averaged over the posterior: P(y''|x'', D) = ∫ P(y''|x'', θ)P(θ|D)dθ.
* '''Conjugate prior''' — A prior whose posterior has the same functional form; enables closed-form updates.
* '''MCMC (Markov Chain Monte Carlo)''' — A family of sampling algorithms for approximating intractable posterior distributions.
* '''Variational inference (VI)''' — Approximates the posterior with a simpler distribution by minimizing KL divergence; faster than MCMC.
* '''Gaussian process (GP)''' — A non-parametric Bayesian model defining a prior over functions; exactly tractable for regression.
* '''Bayesian neural network (BNN)''' — A neural network with distributions over weights, enabling uncertainty estimation.
* '''Monte Carlo Dropout''' — Approximates Bayesian uncertainty by running inference with dropout enabled at test time.
* '''Bayesian optimization''' — Using a probabilistic surrogate model (usually GP) to optimize expensive black-box functions.
* '''Epistemic uncertainty''' — Uncertainty due to lack of knowledge (data); can be reduced with more data.
* '''Aleatoric uncertainty''' — Irreducible uncertainty from inherent randomness in the data-generating process.
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