# 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.

After that, consider visiting the Bayesian update page.

Children:

• 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

Parents:

• Probability theory

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