Approximating hidden Gaussian Markov random fields Export

@article{citeulike:399819, abstract = { Summary. Gaussian Markov random-field (GMRF) models are frequently used in a wide variety of applications. In most cases parts of the GMRF are observed through mutually independent data; hence the full conditional of the GMRF, a hidden GMRF (HGMRF), is of interest. We are concerned with the case where the likelihood is non-Gaussian, leading to non-Gaussian HGMRF models. Several researchers have constructed block sampling Markov chain Monte Carlo schemes based on approximations of the HGMRF by a GMRF, using a second-order expansion of the log-density at or near the mode. This is possible as the GMRF approximation can be sampled exactly with a known normalizing constant. The Markov property of the GMRF approximation yields computational efficiency.The main contribution in the paper is to go beyond the GMRF approximation and to construct a class of non-Gaussian approximations which adapt automatically to the particular HGMRF that is under study. The accuracy can be tuned by intuitive parameters to nearly any precision. These non-Gaussian approximations share the same computational complexity as those which are based on GMRFs and can be sampled exactly with computable normalizing constants. We apply our approximations in spatial disease mapping and model-based geostatistical models with different likelihoods, obtain procedures for block updating and construct Metropolized independence samplers.}, author = {Rue, Havard and Steinsland, Ingelin and Erland, Sveinung}, citeulike-article-id = {399819}, citeulike-linkout-0 = {http://dx.doi.org/10.1111/j.1467-9868.2004.B5590.x}, citeulike-linkout-1 = {http://www.ingentaconnect.com/content/bpl/rssb/2004/00000066/00000004/art00004}, doi = {10.1111/j.1467-9868.2004.B5590.x}, issn = {1369-7412}, journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)}, keywords = {grf, hgmrf, markov}, month = {November}, number = {4}, pages = {877--892}, posted-at = {2009-01-18 19:57:14}, priority = {0}, title = {Approximating hidden Gaussian Markov random fields}, url = {http://dx.doi.org/10.1111/j.1467-9868.2004.B5590.x}, volume = {66}, year = {2004} }

TY - JOUR ID - citeulike:399819 L3 - citeulike-article-id:399819 N2 - Summary. Gaussian Markov random-field (GMRF) models are frequently used in a wide variety of applications. In most cases parts of the GMRF are observed through mutually independent data; hence the full conditional of the GMRF, a hidden GMRF (HGMRF), is of interest. We are concerned with the case where the likelihood is non-Gaussian, leading to non-Gaussian HGMRF models. Several researchers have constructed block sampling Markov chain Monte Carlo schemes based on approximations of the HGMRF by a GMRF, using a second-order expansion of the log-density at or near the mode. This is possible as the GMRF approximation can be sampled exactly with a known normalizing constant. The Markov property of the GMRF approximation yields computational efficiency.The main contribution in the paper is to go beyond the GMRF approximation and to construct a class of non-Gaussian approximations which adapt automatically to the particular HGMRF that is under study. The accuracy can be tuned by intuitive parameters to nearly any precision. These non-Gaussian approximations share the same computational complexity as those which are based on GMRFs and can be sampled exactly with computable normalizing constants. We apply our approximations in spatial disease mapping and model-based geostatistical models with different likelihoods, obtain procedures for block updating and construct Metropolized independence samplers. IS - 4 JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology) SN - 1369-7412 EP - 892 TI - Approximating hidden Gaussian Markov random fields VL - 66 SP - 877 KW - grf KW - hgmrf KW - markov AU - Rue, Havard AU - Steinsland, Ingelin AU - Erland, Sveinung PY - 2004/11// UR - http://dx.doi.org/10.1111/j.1467-9868.2004.B5590.x ER -