Bayesian Machine Learning applies probabilistic reasoning to machine learning by treating model parameters as random variables with prior beliefs that update into posterior distributions given observed data. Unlike frequentist approaches that seek single point estimates, Bayesian methods provide full uncertainty quantification over predictions and parameters, enabling principled decision-making under uncertainty. The framework revolves around Bayes' theorem—combining prior knowledge with likelihood to compute posteriors—and requires inference algorithms (MCMC, variational methods) when exact computation is intractable. Mastering this paradigm means understanding how priors encode assumptions, how inference scales to complex models, and how uncertainty propagates through predictions.
What This Cheat Sheet Covers
This topic spans 13 focused tables and 87 indexed concepts. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.
Table 1: Bayesian Inference Fundamentals
Core concepts that define the Bayesian approach to learning from data. Bayes' theorem provides the mathematical foundation, while the interplay between prior, likelihood, and posterior determines how beliefs update. Understanding these elements is essential before applying any Bayesian method.
| Concept | Example | Description |
|---|---|---|
p(\theta | D) = \frac{p(D | \theta) p(\theta)}{p(D)} | Posterior equals likelihood times prior divided by evidence; foundation of Bayesian inference updating beliefs with data | |
p(\theta) | Encodes beliefs about parameters before observing data; choice impacts posterior when data is limited | |
p(D | \theta) | Probability of observed data given parameters; measures how well parameters explain observations | |
p(\theta | D) | Updated beliefs after observing data; combines prior and likelihood into refined parameter estimate |