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'''Conjugation''' or '''conjugate''' may refer to: *[[Conjugate (square roots)]], the change of sign of a square root in an expression ...

...d B. |last6=Rubin |display-authors=1 |chapter=Normal data with a conjugate prior distribution |pages=67–68 |title=Bayesian Data Analysis |edition=Third |pub ==Related distributions== ...

{{short description|Two-parameter family of continuous probability distributions}} ...ce, which allows the gamma distribution to be used directly as a conjugate prior. Other Bayesians prefer to parametrize the inverse gamma distribution diff ...

{{Short description|Family of continuous probability distributions}} ...=[[Image:GIG distribution pdf.svg|325px|Probability density plots of GIG distributions]]| ...

...uous- or discrete-valued [[Bayesian networks]], with [[conjugate exponents|conjugate-exponential]] parents, developed by John Winn. VMP was developed as a means where <math>\mathbb{E}_{-j}\{\ln P(H,V)\}</math> is the expectation over all distributions <math>Q_i</math> except <math>Q_j</math>. Thus, if we set <math>Q_j</math> ...

This family of scaled inverse chi-squared distributions is linked to the [[inverse-chi-squared distribution]] and to the [[chi-squa This family of scaled inverse chi-squared distributions is a reparametrization of the [[inverse-gamma distribution]]. ...

...espect to that likelihood function and the prior is called a '''conjugate prior''' for the likelihood function <math>p(x \mid \theta)</math>. ...Further, conjugate priors may clarify how a likelihood function updates a prior distribution. ...

...n expressed as a probability, the beta prime distribution is the conjugate prior distribution of the parameter of a Bernoulli distribution expressed in [[od ...>{{cite journal|last=Dubey|first=Satya D.|title=Compound gamma, beta and F distributions|journal=Metrika|date=December 1970|volume=16|pages=27–31|doi=10.1007/BF0261 ...

...r bet on the outcome in this case, there is no advantage to be gained with prior knowledge of the probabilities. In this case, the entropy is maximum at a v ===Convex conjugate=== ...

**[[Prior distribution]] **[[Conjugate prior]] ...

...and low values of <math>p,</math> but for <math>p=1/2</math> the two-point distributions including the Bernoulli distribution have a lower [[excess kurtosis]], name The Bernoulli distributions for <math>0 \le p \le 1</math> form an [[exponential family]]. ...

...sian statistics]] in which case <math>p(\theta\mid\alpha)</math> is called prior density and <math>p(\mathbf{X}\mid\theta)</math> is the likelihood. Recogni ...>{{Dubious|1=Frequentist_marginal_likelihood|reason=Parameters do not have distributions in frequentists statistics|date=February 2023}}, it is often desirable to c ...

...ematics)|optimization objective]] which incorporates a [[Prior_probability|prior]] [[Probability_density_function|density]] over the quantity one wants to e Now assume that a [[prior distribution]] <math>g</math> over <math>\theta</math> exists. This allows ...

{{Short description|Non-informative prior distribution}} ...{{cite journal | vauthors = Jeffreys H | title = An invariant form for the prior probability in estimation problems | journal = Proceedings of the Royal Soc ...

| title = Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images ...e Bayesian networks are typically specified as a collection of conditional distributions. ...

...s include '''Wishart ensemble''' (in [[random matrix theory]], probability distributions over matrices are usually called "ensembles"), or '''Wishart–Laguerre ensem ...ference|Bayesian statistics]], the Wishart distribution is the [[conjugate prior]] of the [[matrix inverse|inverse]] [[covariance matrix|covariance-matrix]] ...

...n statistics]], and in fact, the Dirichlet distribution is the [[conjugate prior]] of the [[categorical distribution]] and [[multinomial distribution]]. ...ple, when a Dirichlet prior over components is called for, but there is no prior knowledge favoring one component over another. Since all elements of the p ...

{{Short description|Family of probability distributions related to the normal distribution}} ...or generality, as exponential families are in a sense very natural sets of distributions to consider. The term '''exponential class''' is sometimes used in place of ...

These two different geometric distributions should not be confused with each other. Often, the name ''shifted'' geometr ...n |url=https://link.springer.com/10.1007/978-3-031-02425-2 |title=Discrete Distributions in Engineering and the Applied Sciences |last2=Shanmugam |first2=Ramalingam ...

...(assuming that [[fair coin|the coin is fair]]). More commonly, probability distributions are used to compare the relative occurrence of many different random values ...be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given ...