Bayesian reasoning

According to its advocates, Bayesian reasoning is a way of seeing the world, and our beliefs about the world, in the light of probability theory, in particular Bayes’s Theorem or Bayes’s Rule. This probability-theoretic way of seeing the world can apply to scientific issues, to tasks in machine learning, and to everyday life.

To start learning, visit Arbital’s Guide to Bayes’s Rule.

After that, consider visiting the Bayesian update page.


  • Bayesian update

    Bayesian updating: the ideal way to change probabilistic beliefs based on evidence.

  • Bayes' rule

    Bayes’ rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.

  • Prior probability

    What we believed before seeing the evidence.

  • Interest in mathematical foundations in Bayesianism

    “Want” this requisite if you prefer to see extra information about the mathematical foundations in Bayesianism.

  • Posterior probability

    What we believe, after seeing the evidence and doing a Bayesian update.

  • Humans doing Bayes

    The human use of Bayesian reasoning in everyday life

  • Ignorance prior

    Key equations for quantitative Bayesian problems, describing exactly the right shape for what we believed before observation.

  • Strictly confused

    A hypothesis is strictly confused by the raw data, if the hypothesis did much worse in predicting it than the hypothesis itself expected.

  • Finishing your Bayesian path on Arbital

    The page that comes at the end of reading the Arbital Guide to Bayes’ rule

  • Prior

    A state of prior knowledge, before seeing information on a new problem. Potentially complicated.

  • Empirical probabilities are not exactly 0 or 1

    “Cromwell’s Rule” says that probabilities of exactly 0 or 1 should never be applied to empirical propositions—there’s always some probability, however tiny, of being mistaken.

  • Subjective probability

    Probability is in the mind, not in the environment. If you don’t know whether a coin came up heads or tails, that’s a fact about you, not a fact about the coin.

  • Likelihood


  • Probability theory

    The logic of science; coherence relations on quantitative degrees of belief.