### Some articles on *distribution, distributions, posterior distribution, posterior*:

Categorical Distribution - With A Conjugate Prior

... In Bayesian statistics, the Dirichlet

... In Bayesian statistics, the Dirichlet

**distribution**is the conjugate prior**distribution**of the categorical**distribution**(and also the multinomial**distribution**) ... This means that in a model consisting of a data point having a categorical**distribution**with unknown parameter vector p, and (in standard Bayesian style) we choose to treat this parameter as a random variable and ... can update our knowledge based on the data point and end up with a new**distribution**of the same form as the old one ...Uninformative Priors

... probability

... probability

**distributions**in some sense logically required by the nature of one's state of uncertainty these are a subject of philosophical controversy, with Bayesians being ... experiment and not to dissolve in another experiment then this prior is updated to the uniform**distribution**on the interval ... prior has been criticized on the grounds that it yields an improper**posterior distribution**that puts 100% of the probability content at either p = 0 or at p = 1 if a finite number of observations have given the ...Categorical Distribution - With A Conjugate Prior - Posterior Predictive Distribution

... The

... The

**posterior**predictive**distribution**of a new observation in the above model is the**distribution**that a new observation would take given the set of N categorical observations ... As shown in the Dirichlet-multinomial**distribution**article, it has a very simple form Note the various relationships among this formula and the previous ones The**posterior**... The**posterior**predictive probability is the same as the expected value of the**posterior distribution**...Exponential Family - Role in Statistics - Bayesian Estimation: Conjugate Distributions

... In Bayesian statistics a prior

... In Bayesian statistics a prior

**distribution**is multiplied by a likelihood function and then normalised to produce a**posterior distribution**... to the effective number of observations that the prior**distribution**contributes, and corresponds to the total amount that these pseudo-observations contribute to the sufficient ... and equivalently are the same functions as in the definition of the**distribution**over which is the conjugate prior ...### Famous quotes containing the word distribution:

“There is the illusion of time, which is very deep; who has disposed of it? Mor come to the conviction that what seems the succession of thought is only the *distribution* of wholes into causal series.”

—Ralph Waldo Emerson (1803–1882)

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