Hyperprior (original) (raw)
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:
| Property | Value |
|---|---|
| dbo:abstract | 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 itself has hyperparameters, these may be called hyperhyperparameters, and so forth. One can analogously call the posterior distribution on the hyperparameter the hyperposterior, and, if these are in the same family, call them conjugate hyperdistributions or a conjugate hyperprior. However, this rapidly becomes very abstract and removed from the original problem. (en) |
| dbo:wikiPageExternalLink | https://books.google.com/books%3Fid=11nSgIcd7xQC |
| dbo:wikiPageID | 21761858 (xsd:integer) |
| dbo:wikiPageLength | 4981 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1114884327 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Bayesian_statistics dbr:Bernoulli_distribution dbr:Hyperparameter dbr:Beta_distribution dbr:Dynamical_system dbr:Convex_set dbr:Conjugate_prior dbr:Convex_combination dbc:Bayesian_statistics dbr:Multilevel_model dbr:Mixture_density dbr:Prior_distribution |
| dbp:wikiPageUsesTemplate | dbt:Cite_book dbt:Reflist dbt:Bayesian_statistics |
| dct:subject | dbc:Bayesian_statistics |
| gold:hypernym | dbr:Distribution |
| rdf:type | dbo:Software |
| rdfs:comment | 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: (en) |
| rdfs:label | Hyperprior (en) |
| owl:sameAs | freebase:Hyperprior wikidata:Hyperprior https://global.dbpedia.org/id/4nDkJ |
| prov:wasDerivedFrom | wikipedia-en:Hyperprior?oldid=1114884327&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Hyperprior |
| is dbo:wikiPageRedirects of | dbr:Hyperprior_distribution |
| is dbo:wikiPageWikiLink of | dbr:Bayesian_hierarchical_modeling dbr:Hyperparameter dbr:Information_field_theory dbr:Conjugate_prior dbr:Comparison_of_Gaussian_process_software dbr:Empirical_Bayes_method dbr:Exponential_family dbr:Dirichlet_distribution dbr:Prior_probability dbr:Categorical_distribution dbr:Expected_utility_hypothesis dbr:List_of_statistics_articles dbr:Hyperprior_distribution |
| is foaf:primaryTopic of | wikipedia-en:Hyperprior |