Convergence Rates of Posterior Distributions for Brownian Semimartingale Models
We consider the asymptotic behaviour of posterior distributions based on continuous observations from a Brownian semimartingale model. We present a general result that bounds the posterior rate of convergence in terms of the complexity of the model and the amount of prior mass given to balls centred...
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| Veröffentlicht in: | Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2006-10, Vol.12 (5), p.863-888 |
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| container_end_page | 888 |
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| container_issue | 5 |
| container_start_page | 863 |
| container_title | Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability |
| container_volume | 12 |
| creator | Van Der Meulen, F. H. Van Der Vaart, A. W. Van Zanten, J. H. |
| description | We consider the asymptotic behaviour of posterior distributions based on continuous observations from a Brownian semimartingale model. We present a general result that bounds the posterior rate of convergence in terms of the complexity of the model and the amount of prior mass given to balls centred around the true parameter. This result is illustrated for three special cases of the model: the Gaussian white noise model, the perturbed dynamical system and the ergodic diffusion model. Some examples for specific priors are discussed as well. |
| doi_str_mv | 10.3150/bj/1161614950 |
| format | Article |
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Some examples for specific priors are discussed as well.</description><subject>Average linear density</subject><subject>Bayesian estimation</subject><subject>continuous semimartingale</subject><subject>Determinism</subject><subject>Dirichlet process</subject><subject>Entropy</subject><subject>Ergodic theory</subject><subject>Hellinger distance</subject><subject>infinite-dimensional model</subject><subject>Martingales</subject><subject>Mathematical functions</subject><subject>Mathematical independent variables</subject><subject>Musical intervals</subject><subject>Parametric models</subject><subject>rate of convergence</subject><subject>wavelets</subject><subject>White noise</subject><issn>1350-7265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNplkE9LAzEUxHNQsFaPHoV8gbXJ5t_uSXS1KlQqas9Lsnlbsmw3JUkVv70tLfUg7zAwzPx4DEJXlNwwKsjEdBNK5fZ4KcgJGlEmSKZyKc7QeYwdIZRLSUZoXvnhC8IShgbwu04QsW_xm48JgvMBP7iYgjOb5PwQcbt17oP_Hpwe8Aes3EqH5Ial7gG_egt9vECnre4jXB50jBbTx8_qOZvNn16qu1nWMMFTZlmuCUjFmNEtZ6WwqlCWtYqCsVyZ0nImAAhRuShloYAKzbRQRspSNIVhY3S7566D76BJsGl6Z-t12L30U3vt6moxO7gHMV39t8mWkO0JTfAxBmiPZUrq3Yb_8tf7fBeTD8dwLrjkBafsF2WkcWo</recordid><startdate>20061001</startdate><enddate>20061001</enddate><creator>Van Der Meulen, F. 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| issn | 1350-7265 |
| language | eng |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; Jstor Complete Legacy; Project Euclid Complete |
| subjects | Average linear density Bayesian estimation continuous semimartingale Determinism Dirichlet process Entropy Ergodic theory Hellinger distance infinite-dimensional model Martingales Mathematical functions Mathematical independent variables Musical intervals Parametric models rate of convergence wavelets White noise |
| title | Convergence Rates of Posterior Distributions for Brownian Semimartingale Models |
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