A Hierarchical Spatio-Temporal Statistical Model Motivated by Glaciology

In this paper, we extend and analyze a Bayesian hierarchical spatio-temporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.Comment: Revision accepted for publication by the Journal of Agricultural, Biological, and Environmental Statistic

A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatiotemporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error-correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.The Icelandic Research Fund (RANNIS) is thanked for funding this research.Peer Reviewe

A Hierarchical Spatiotemporal Statistical Model Motivated by Glaciology

This is a post-peer-review, pre-copyedit version of an article published in Journal of Agricultural, Biological and Environmental Statistics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s13253-019-00367-1In this paper, we extend and analyze a Bayesian hierarchical spatiotemporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.Icelandic Centre for Research (152457).Peer reviewe

A probabilistic geologic model of the Krafla geothermal system constrained by gravimetric data

Publisher's version (útgefin grein).The quantitative connections between subsurface geologic structure and measured geophysical data allow 3D geologic models to be tested against measurements and geophysical anomalies to be interpreted in terms of geologic structure. Using a Bayesian framework, geophysical inversions are constrained by prior information in the form of a reference geologic model and probability density functions (pdfs) describing petrophysical properties of the different lithologic units. However, it is challenging to select the probabilistic weights and the structure of the prior model in such a way that the inversion process retains relevant geologic insights from the prior while also exploring the full range of plausible subsurface models. In this study, we investigate how the uncertainty of the prior (expressed using probabilistic constraints on commonality and shape) controls the inferred lithologic and mass density structure obtained by probabilistic inversion of gravimetric data measured at the Krafla geothermal system. We combine a reference prior geologic model with statistics for rock properties (grain density and porosity) in a Bayesian inference framework implemented in the GeoModeller software package. Posterior probability distributions for the inferred lithologic structure, mass density distribution, and uncertainty quantification metrics depend on the assumed geologic constraints and measurement error. As the uncertainty of the reference prior geologic model increases, the posterior lithologic structure deviates from the reference prior model in areas where it may be most likely to be inconsistent with the observed gravity data and may need to be revised. In Krafla, the strength of the gravity field reflects variations in the thickness of hyaloclastite and the depth to high-density basement intrusions. Moreover, the posterior results suggest that a WNW–ESE-oriented gravity low that transects the caldera may be associated with a zone of low hyaloclastite density. This study underscores the importance of reliable prior constraints on lithologic structure and rock properties during Bayesian geophysical inversion.Icelandic Centre for Research. This study was funded by Technical Development Fund of the Research Center of Iceland (RANNÍS—Grant Number 175193-0612 Data Fusion for Geothermal Reservoir Characterization).Peer Reviewe

A genome-wide scan for preeclampsia in the Netherlands

Preeclampsia, hallmarked by de novo hypertension and proteinuria in pregnancy, has a familial tendency. Recently, a large Icelandic genome-wide scan provided evidence for a maternal susceptibility locus for preeclampsia on chromosome 2p13 which was confirmed by a genome scan from Australia and New Zealand (NZ). The current study reports on a genome-wide scan of Dutch affected sib-pair families. In total 67 Dutch affected sib-pair families, comprising at least two siblings with proteinuric preeclampsia, eclampsia or HELLP-syndrome, were typed for 293 polymorphic markers throughout the genome and linkage analysis was performed. The highest allele sharing lod score of 1.99 was seen on chromosome 12q at 109.5 cM. Two peaks overlapped in the same regions between the Dutch and Icelandic genome-wide scan at chromosome 3p and chromosome 15q. No overlap was seen on 2p. Re-analysis in 38 families without HELLP-syndrome (preeclampsia families) and 34 families with at least one sibling with HELLP syndrome (HELLP families), revealed two peaks with suggestive evidence for linkage in the non-HELLP families on chromosome 10q (lod score 2.38, D10S1432, 93.9 cM) and 22q (lod score 2.41, D22S685, 32.4 cM). The peak on 12q appeared to be associated with HELLP syndrome; it increased to a lod score of 2.1 in the HELLP families and almost disappeared in the preeclampsia families. A nominal peak on chromosome 11 in the preeclampsia families showed overlap with the second highest peak in the Australian/NZ study. Results from our Dutch genome-wide scan indicate that HELLP syndrome might have a different genetic background than preeclampsia.Augusta MA Lachmeijer, Reynir Arngrímsson, Esther J Bastiaans, Michael L Frigge, Gerald Pals, Sigrun Sigurdardóttir, Hreinn Stéfansson, Birgir Pálsson, Dan Nicolae, Augustin Kong, Jan G Aarnoudse, Jeff R Gulcher, Guustaaf A Dekker, Leo P ten Kate and Kári Stéfansso