# Posterior Distribution

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

Categorical Distribution - With A Conjugate Prior
... 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 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 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 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)