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  • Neal_Kypraios_2014

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Exact Bayesian inference via data augmentation

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Exact Bayesian inference via data augmentation. / Neal, Peter; Kypraios, Theodore.
In: Statistics and Computing, Vol. 25, No. 2, 03.2015, p. 333-347.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Neal, P & Kypraios, T 2015, 'Exact Bayesian inference via data augmentation', Statistics and Computing, vol. 25, no. 2, pp. 333-347. https://doi.org/10.1007/s11222-013-9435-z

APA

Neal, P., & Kypraios, T. (2015). Exact Bayesian inference via data augmentation. Statistics and Computing, 25(2), 333-347. https://doi.org/10.1007/s11222-013-9435-z

Vancouver

Neal P, Kypraios T. Exact Bayesian inference via data augmentation. Statistics and Computing. 2015 Mar;25(2):333-347. Epub 2013 Dec 3. doi: 10.1007/s11222-013-9435-z

Author

Neal, Peter ; Kypraios, Theodore. / Exact Bayesian inference via data augmentation. In: Statistics and Computing. 2015 ; Vol. 25, No. 2. pp. 333-347.

Bibtex

@article{2e4bc5cd78494e639766fa7ccc419a6f,
title = "Exact Bayesian inference via data augmentation",
abstract = "Data augmentation is a common tool in Bayesian statistics, especially in the application of MCMC. Data augmentation is used where direct computation of the posterior density, π(θ|x), of the parameters θ, given the observed data x, is not possible. We show that for a range of problems, it is possible to augment the data by y, such that, π(θ|x,y) is known, and π(y|x) can easily be computed. In particular, π(y|x) is obtained by collapsing π(y,θ|x) through integrating out θ. This allows the exact computation of π(θ|x) as a mixture distribution without recourse to approximating methods such as MCMC. Useful byproducts of the exact posterior distribution are the marginal likelihood of the model and the exact predictive distribution.",
keywords = "Bayesian statistics, Data augmentation, Multinomial distribution, Reed-Frost epidemic, Integer valued autoregressive process",
author = "Peter Neal and Theodore Kypraios",
note = "{\textcopyright} The Author(s) 2013. This article is published with open access at Springerlink.com ",
year = "2015",
month = mar,
doi = "10.1007/s11222-013-9435-z",
language = "English",
volume = "25",
pages = "333--347",
journal = "Statistics and Computing",
issn = "0960-3174",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - Exact Bayesian inference via data augmentation

AU - Neal, Peter

AU - Kypraios, Theodore

N1 - © The Author(s) 2013. This article is published with open access at Springerlink.com

PY - 2015/3

Y1 - 2015/3

N2 - Data augmentation is a common tool in Bayesian statistics, especially in the application of MCMC. Data augmentation is used where direct computation of the posterior density, π(θ|x), of the parameters θ, given the observed data x, is not possible. We show that for a range of problems, it is possible to augment the data by y, such that, π(θ|x,y) is known, and π(y|x) can easily be computed. In particular, π(y|x) is obtained by collapsing π(y,θ|x) through integrating out θ. This allows the exact computation of π(θ|x) as a mixture distribution without recourse to approximating methods such as MCMC. Useful byproducts of the exact posterior distribution are the marginal likelihood of the model and the exact predictive distribution.

AB - Data augmentation is a common tool in Bayesian statistics, especially in the application of MCMC. Data augmentation is used where direct computation of the posterior density, π(θ|x), of the parameters θ, given the observed data x, is not possible. We show that for a range of problems, it is possible to augment the data by y, such that, π(θ|x,y) is known, and π(y|x) can easily be computed. In particular, π(y|x) is obtained by collapsing π(y,θ|x) through integrating out θ. This allows the exact computation of π(θ|x) as a mixture distribution without recourse to approximating methods such as MCMC. Useful byproducts of the exact posterior distribution are the marginal likelihood of the model and the exact predictive distribution.

KW - Bayesian statistics

KW - Data augmentation

KW - Multinomial distribution

KW - Reed-Frost epidemic

KW - Integer valued autoregressive process

U2 - 10.1007/s11222-013-9435-z

DO - 10.1007/s11222-013-9435-z

M3 - Journal article

VL - 25

SP - 333

EP - 347

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 2

ER -