Hyperprior

	Hyperprior In Bayesian statistics, a hyperprior is a prior distribution on a hyperparameter, that is, on a parameter of a prior distribution. As with the term ''hyperparameter,'' the use of ''hyper'' is to distinguish it from a prior distribution of a parameter of the model for the underlying system. They arise particularly in the use of hierarchical models. For example, if one is using a beta distribution to model the distribution of the parameter ''p'' of a Bernoulli distribution, then: * The Bernoulli distribution (with parameter ''p'') is the ''model'' of the underlying system; * ''p'' is a ''parameter'' of the underlying system (Bernoulli distribution); * The beta distribution (with parameters ''α'' and ''β'') is the ''prior'' distribution of ''p''; * ''α'' and ''β'' are parameters of the prior distribution (beta distribution), hence ''hyperparameters;'' * A prior distribution of ''α'' and ''β'' is thus a ''hyperprior.'' In principle, one can iterate the above: if the hyperprior ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Hyperparameter In Bayesian statistics, a hyperparameter is a parameter of a prior distribution; the term is used to distinguish them from parameters of the model for the underlying system under analysis. For example, if one is using a beta distribution to model the distribution of the parameter ''p'' of a Bernoulli distribution, then: * ''p'' is a parameter of the underlying system (Bernoulli distribution), and * ''α'' and ''β'' are parameters of the prior distribution (beta distribution), hence ''hyper''parameters. One may take a single value for a given hyperparameter, or one can iterate and take a probability distribution on the hyperparameter itself, called a hyperprior. Purpose One often uses a prior which comes from a parametric family of probability distributions – this is done partly for explicitness (so one can write down a distribution, and choose the form by varying the hyperparameter, rather than trying to produce an arbitrary function), and partly so that one can ''vary'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Prior Distribution In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable. Bayes' theorem calculates the renormalized pointwise product of the prior and the likelihood function, to produce the '' posterior probability distribution'', which is the conditional distribution of the uncertain quantity given the data. Similarly, the prior probability of a random event or an uncertain proposition is the unconditional probability that is assigned before any relevant evidence is taken into account. Priors can be created using a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Bayesian Statistics Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation that views probability as the limit of the relative frequency of an event after many trials. Bayesian statistical methods use Bayes' theorem to compute and update probabilities after obtaining new data. Bayes' theorem describes the conditional probability of an event based on data as well as prior information or beliefs about the event or conditions related to the event. For example, in Bayesian inference, Bayes' theorem can be used to estimate the parameters of a probability distribution or statistical model. Since Bayesian statistics treats probabi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]