What is Bayesian inference in machine learning?

Bayesian inference treats model parameters as random variables with prior distributions (beliefs before seeing data). After observing data, we update to the posterior distribution using Bayes' theorem: P(θ|data) ∝ P(data|θ) × P(θ). Instead of a single point estimate for parameters, Bayesian methods provide a full distribution, quantifying uncertainty. This is valuable in low-data regimes and for safety-critical applications where knowing model uncertainty matters. Challenges: computing the posterior is often intractable, requiring approximate methods like MCMC or Variational Inference.