🔁 Bayesian Inference.

Bayesian Inference.#

Updating beliefs about parameters using priors and observed data.

Important

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What it is#

Bayesian inference updates beliefs in light of evidence using Bayes’ theorem — it combines a prior (what you believed before) with the likelihood (how probable the data are under each hypothesis) to produce a posterior (what you believe after):

\[\text{posterior} \propto \text{prior} \times \text{likelihood}.\]

Parameters are treated as random variables with distributions, not fixed points.

What makes it distinctive#

Because it yields a full posterior distribution, Bayesian inference quantifies uncertainty directly — a credible interval says there’s a 95% probability the parameter lies inside it — and it naturally incorporates prior knowledge and updates sequentially as data arrive. This contrasts with the frequentist view of fixed parameters and p-values.

The catch and the tools#

Posteriors are usually intractable, so they’re approximated with Markov Chain Monte Carlo or variational methods via tools like Stan, PyMC, or NumPyro. Bayesian inference underlies Bayesian A/B testing, Bayesian optimization, and the causal tree models above.

Theme: Bayesian Inference · All terminology

Hint

Mind map — connected ideas

Causal Trees · Likelihood · Normal Distribution · Statistical Tests · Confidence Intervals (CIs) · Uplift Random Forests

Hint

More in Bayesian Inference

Bayes’ Theorem · Bayesian Correction · Bayesian Decision Theory (BDT) · Bayesian Neural Networks (BNNs) · Binomial Likelihood · Gaussian Processes (GPs) · Marginal Likelihood (also called The Model Evidence or Integrated Likelihood) · MCMC (Markov Chain Monte Carlo) · Parameter(s) of Interest · Posterior · Posterior belief · Posterior Probability · Posterior probability of uplift · Prior Belief (or Prior Probability)