probability theory

Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory.

Bayes Theorem (also known as Bayes Rule, or Bayes Formula)

Bayes Theorem (also known as Bayes Rule, or Bayes Formula) was discovered by Thomas Bayes, a monk who died in the mid-18th century.

conditional probabilities

Bayes rule is used for conditional probabilities which occurs frequently in business problems.

on Bayes rule of conditional probability

This is based on Bayes rule of conditional probability.

a theorem in probability theory that answers the question, 'When you encounter new information, how much should new informationchange your confidence in a belief

Bayes’s Rule is a theorem in probability theory that answers the question, 'When you encounter new information, how much should new informationchange your confidence in a belief?'

manipulation of conditional probabilities

Bayes rule is used in naive bayes algorithm for the manipulation of conditional probabilities.

the conditional probability of a given event, computed after observing a second event whose conditional and unconditional probabilities were known in advance

Bayes' rule is the conditional probability of a given event, computed after observing a second event whose conditional and unconditional probabilities were known in advance.

The normative method for integrating base rates

The normative method for integrating base rates (prior probabilities) and featural evidence (likelihoods) is given by Bayes rule.

one of the fundamental Theorems of statistics

Bayes’ Rule is one of the fundamental Theorems of statistics, but up until recently, I have to admit, I was never very impressed with statistics.

a simple formula from probability theory for inferring how much one should adjust one’s beliefs, in this probabilistic sense, given some overall likelihood and current evidence

Bayes rule is a simple formula from probability theory for inferring how much one should adjust one’s beliefs, in this probabilistic sense, given some overall likelihood and current evidence.

a simple tautology of probability theory

When stated in terms of abstract random variables , Bayes ' rule is a simple tautology of probability theory .

just a mathematical identity in probability theory

By itself, Bayes' rule is just a mathematical identity in probability theory.

allows unknown probabilities to be computed from known conditional probabilities

Bayes’ rule allows unknown probabilities to be computed from known conditional probabilities, usually in the causal direction.

the one , which maximizes expected utility

Formally, Bayesian inference is calibrated with reference to an explicitly stated utility, or loss function; the 'Bayes rule' is the one which maximizes expected utility, averaged over the posterior uncertainty.

of belief

Rather than trying to solve incredibly complex situations all at once, Bayes Rule represents a state of belief, or knowledge, by cutting a system up into more digestible pieces, where knowledge can be accumulated along the way.

a simple reliability-weighted summation model of cue combination

Under the assumption of Gaussian distributed independent estimates, Bayes rule provides a simple reliability-weighted summation model of cue combination.

a simple 17th century theory for the evaluation of knowledge

Bayes rule is a simple 17th century theory for the evaluation of knowledge, criticized for most of the 20th century.

the link that allows us to go between the two situations

these two probabilities turns out that Bayes' rule is the link that allows us to go between the two situations.

the posterior odds of two alternatives

Stated in terms of odds, Bayes' rule is that the posterior odds of two alternatives, and , given an event , is the prior odds, times the likelihood ratio.

the only legitimate form of learning from experience

Along the way, Huttegger addresses a number of debates in epistemology and the philosophy of science, including the status of prior probabilities, whether Bayes' rule is the only legitimate form of learning from experience, and whether rational agents can have sustained disagreements.