1.24 Bayesian inference in practice
You can fit a small Bayesian model and interpret the posterior.
Before:00. Orientation & SetupUnlocks:03. Data Handling & Analysis04. Classical AI — Agents, Search & Knowledge Representation
Bayesian inference treats parameters as uncertain quantities and returns whole distributions instead of point estimates — often exactly what a decision needs. Fitting one small model in PyMC or NumPyro makes priors and posteriors concrete instead of philosophical. It closes the statistics run as the advanced alternative lens. The confusion to manage is expecting exactness: real posteriors come from MCMC or variational approximation, and knowing the machinery is approximate is part of using it honestly.
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Conjugate priors and closed forms
Some prior and likelihood pairs combine into a posterior of the same family, which makes the arithmetic exact and instructive. These cases are where Bayesian reasoning is best learned.
MCMC and variational inference — the idea
When exact answers are unavailable, the posterior is either sampled from or approximated by a simpler distribution. Understanding what each approach trades is enough at this level.
PyMC or NumPyro on a real dataset
Fitting a small model with a probabilistic programming library on real data, which is where the ideas stop being abstract. The output is a distribution rather than a single number.
Credible intervals vs. confidence intervals
A credible interval says where the parameter probably is; a confidence interval says something about the procedure. This is the cleanest illustration of the difference between the two philosophies.
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