Bayesian Inference

Wed, 11 Nov 2026 13:50:00 +1100

This page condenses UNSW MATH5960 (Bayesian Inference and Computation). It assumes the Probability page and sits under Statistics, whose table of distributions it uses throughout. Gamma distributions are in the rate parameterisation: \(\mathrm{Gamma}(a,b)\) has density \(\frac{b^a}{\Gamma(a)}\theta^{a-1}e^{-b\theta}\), mean \(a/b\) and variance \(a/b^2\).

The course has two halves that keep meeting. One is modelling: write a likelihood and a prior, get a posterior, and answer every question with an integral against it. The other is computation: when those integrals have no closed form, replace them by averages over draws, first independent (Monte Carlo, inversion, rejection, importance sampling), then dependent (Gibbs and Metropolis-Hastings). The last third uses both halves on model comparison, hierarchical models and mixtures.

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Bayesian Inference