Rights statement: © The Author(s) 2013. This article is published with open access at Springerlink.com
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -