Max-and-Smooth: a two-step approach for approximate Bayesian inference in latent Gaussian models
dc.contributor.author | Hrafnkelsson, B | |
dc.contributor.author | Siegert, S | |
dc.contributor.author | Huser, R | |
dc.contributor.author | Bakka, H | |
dc.contributor.author | Jóhannesson, ÁV | |
dc.date.accessioned | 2020-07-17T11:00:34Z | |
dc.date.issued | 2020-06-19 | |
dc.description.abstract | With modern high-dimensional data, complex statistical models are necessary, requiring computationally feasible inference schemes. We introduce Max-and-Smooth, an approximate Bayesian inference scheme for a flexible class of latent Gaussian models (LGMs) where one or more of the likelihood parameters are modeled by latent additive Gaussian processes. Max-and-Smooth consists of two-steps. In the first step (Max), the likelihood function is approximated by a Gaussian density with mean and covariance equal to either (a) the maximum likelihood estimate and the inverse observed information, respectively, or (b) the mean and covariance of the normalized likelihood function. In the second step (Smooth), the latent parameters and hyperparameters are inferred and smoothed with the approximated likelihood function. The proposed method ensures that the uncertainty from the first step is correctly propagated to the second step. Since the approximated likelihood function is Gaussian, the approximate posterior density of the latent parameters of the LGM (conditional on the hyperparameters) is also Gaussian, thus facilitating efficient posterior inference in high dimensions. Furthermore, the approximate marginal posterior distribution of the hyperparameters is tractable, and as a result, the hyperparameters can be sampled independently of the latent parameters. In the case of a large number of independent data replicates, sparse precision matrices, and high-dimensional latent vectors, the speedup is substantial in comparison to an MCMC scheme that infers the posterior density from the exact likelihood function. The proposed inference scheme is demonstrated on one spatially referenced real dataset and on simulated data mimicking spatial, temporal, and spatio-temporal inference problems. Our results show that Max-and-Smooth is accurate and fast. | en_GB |
dc.description.sponsorship | NERC | en_GB |
dc.identifier.citation | Published online 19 June 2020 | en_GB |
dc.identifier.doi | 10.1214/20-BA1219 | |
dc.identifier.uri | http://hdl.handle.net/10871/121990 | |
dc.language.iso | en | en_GB |
dc.publisher | International Society for Bayesian Analysis (ISBA) | en_GB |
dc.rights | © 2020 International Society for Bayesian Analysis. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. | en_GB |
dc.subject | approximate Bayesian inference | en_GB |
dc.subject | Bayesian hierarchical model | en_GB |
dc.subject | latent Gaussian model | en_GB |
dc.subject | multivariate link function | en_GB |
dc.subject | spatio-temporal data | en_GB |
dc.title | Max-and-Smooth: a two-step approach for approximate Bayesian inference in latent Gaussian models | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2020-07-17T11:00:34Z | |
dc.identifier.issn | 1936-0975 | |
dc.description | This is the final version. Available on open access from International Society for Bayesian Analysis (ISBA) via the DOI in this record. | en_GB |
dc.identifier.eissn | 1931-6690 | |
dc.identifier.journal | Bayesian Analysis | en_GB |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_GB |
rioxxterms.version | VoR | en_GB |
rioxxterms.licenseref.startdate | 2020-06-19 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2020-07-17T10:55:44Z | |
refterms.versionFCD | VoR | |
refterms.dateFOA | 2020-07-17T11:00:38Z | |
refterms.panel | B | en_GB |
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Except where otherwise noted, this item's licence is described as © 2020 International Society for Bayesian Analysis. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.