Laplace's rule of succession (as a special case)

E1002836

Bayesian inference rule classical Bayesian method probability estimation method statistical rule

Laplace's rule of succession is a classical Bayesian rule for estimating the probability of an event based on observed successes and failures, assigning a nonzero prior probability to unobserved outcomes.

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Observed surface forms (1)

Surface form	Occurrences
Laplace's rule of succession	0

Statements (47)

Predicate	Object
instanceOf	Bayesian inference rule ⓘ classical Bayesian method ⓘ probability estimation method ⓘ statistical rule ⓘ
addresses	problem of zero counts in probability estimation ⓘ
aimsTo	avoid assigning probability 0 or 1 from finite data ⓘ
appliesTo	Bernoulli trials NERFINISHED ⓘ binary events ⓘ
assumes	exchangeable trials ⓘ independent and identically distributed trials ⓘ no prior information favoring success or failure ⓘ unknown event probability ⓘ
category	Bayesian updating rule NERFINISHED ⓘ probability smoothing technique ⓘ
contrastsWith	maximum likelihood estimate s/n ⓘ
estimates	posterior mean of event probability ⓘ
example	sunrise problem ⓘ
field	Bayesian statistics ⓘ probability theory ⓘ statistical inference ⓘ
formula	(s+1)/(n+2) ⓘ
generalizedBy	Dirichlet prior for multinomial outcomes ⓘ
givesPosterior	Beta(s+1,n-s+1) ⓘ
historicalContext	introduced in the 18th–19th century ⓘ
input	number of observed successes s ⓘ number of trials n ⓘ
interpretation	posterior mean under uniform prior ⓘ predictive probability of success in next trial ⓘ
mathematicalForm	posterior mean of Beta(s+1,n-s+1) distribution ⓘ
namedAfter	Pierre-Simon Laplace NERFINISHED ⓘ
output	estimated probability of success in next trial ⓘ
property	assigns nonzero probability to unobserved outcomes ⓘ asymptotically approaches empirical frequency s/n ⓘ shrinks estimates toward 1/2 for small samples ⓘ
relatedTo	Bayesian predictive distribution NERFINISHED ⓘ Dirichlet-multinomial model NERFINISHED ⓘ Laplace's law of succession NERFINISHED ⓘ add-one smoothing ⓘ principle of insufficient reason ⓘ
specialCaseOf	Bayesian estimation with Beta prior ⓘ conjugate prior analysis for Bernoulli model ⓘ
usedFor	handling zero-frequency problems ⓘ predicting next outcome probability ⓘ smoothing probability estimates ⓘ
usesLikelihood	Binomial likelihood ⓘ
usesPrior	Beta(1,1) prior ⓘ uniform prior on probability parameter ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Carnap's continuum of inductive methods → hasMember → Laplace's rule of succession (as a special case) ⓘ