Multi-Scale Process Modelling and Distributed Computation for Spatial Data

Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that modelling and prediction using infinite-dimensional process models is not possible with large data sets, and that both approximate models and, often, approximate-inference methods, are needed. The problem of fitting simple global spatial models to large data sets has been solved through the likes of multi-resolution approximations and nearest-neighbour techniques. Here we tackle the next challenge, that of fitting complex, nonstationary, multi-scale models to large data sets. We propose doing this through the use of superpositions of spatial processes with increasing spatial scale and increasing degrees of nonstationarity. Computation is facilitated through the use of Gaussian Markov random fields and parallel Markov chain Monte Carlo based on graph colouring. The resulting model allows for both distributed computing and distributed data. Importantly, it provides opportunities for genuine model and data scaleability and yet is still able to borrow strength across large spatial scales. We illustrate a two-scale version on a data set of sea-surface temperature containing on the order of one million observations, and compare our approach to state-of-the-art spatial modelling and prediction methods.Comment: 33 pages, 10 figures, 1 tabl

A sparse linear algebra algorithm for fast computation of prediction variances with Gaussian Markov random fields

Gaussian Markov random fields are used in a large number of disciplines in machine vision and spatial statistics. The models take advantage of sparsity in matrices introduced through the Markov assumptions, and all operations in inference and prediction use sparse linear algebra operations that scale well with dimensionality. Yet, for very high-dimensional models, exact computation of predictive variances of linear combinations of variables is generally computationally prohibitive, and approximate methods (generally interpolation or conditional simulation) are typically used instead. A set of conditions are established under which the variances of linear combinations of random variables can be computed exactly using the Takahashi recursions. The ensuing computational simplification has wide applicability and may be used to enhance several software packages where model fitting is seated in a maximum-likelihood framework. The resulting algorithm is ideal for use in a variety of spatial statistical applications, including \emph{LatticeKrig} modelling, statistical downscaling, and fixed rank kriging. It can compute hundreds of thousands exact predictive variances of linear combinations on a standard desktop with ease, even when large spatial GMRF models are used.Comment: 20 pages, 5 figure

An assessment of forward and inverse GIA solutions for Antarctica

In this work we assess the most recent estimates of glacial isostatic adjustment (GIA) for Antarctica, including those from both forward and inverse methods. The assessment is based on a comparison of the estimated uplift rates with a set of elastic-corrected GPS vertical velocities. These have been observed from an extensive GPS network and computed using data over the period 2009-2014. We find systematic underestimations of the observed uplift rates in both inverse and forward methods over specific regions of Antarctica characterized by low mantle viscosities and thin lithosphere, such as the northern Antarctic Peninsula and the Amundsen Sea Embayment, where its recent ice discharge history is likely to be playing a role in current GIA. Uplift estimates for regions where many GIA models have traditionally placed their uplift maxima, such as the margins of Filchner-Ronne and Ross ice shelves, are found to be overestimated. GIA estimates show large variability over the interior of East Antarc tica which results in increased uncertainties on the ice-sheet mass balance derived from gravimetry methods

Constraining the mass balance of East Antarctica

We investigate the mass balance of East Antarctica for the period 2003-2013 using a Bayesian statistical framework. We combine satellite altimetry, gravimetry, and GPS with prior assumptions characterizing the underlying geophysical processes. We run three experiments based on two different assumptions to study possible solutions to the mass balance. We solve for trends in surface mass balance, ice dynamics, and glacial isostatic adjustment. The first assumption assigns low probability to ice dynamic mass loss in regions of slow flow, giving a mean dynamic trend of 17 ± 10 Gt yr-1 and a total mass imbalance of 57 ± 20 Gt yr-1. The second assumption considers a long-term dynamic thickening hypothesis and an a priori solution for surface mass balance from a regional climate model. The latter results in estimates 3 to 5 times larger for the ice dynamic trends but similar total mass imbalance. In both cases, gains in East Antarctica are smaller than losses in West Antarctica

Heritability and Tissue Specificity of Expression Quantitative Trait Loci

Variation in gene expression is heritable and has been mapped to the genome in humans and model organisms as expression quantitative trait loci (eQTLs). We applied integrated genome-wide expression profiling and linkage analysis to the regulation of gene expression in fat, kidney, adrenal, and heart tissues using the BXH/HXB panel of rat recombinant inbred strains. Here, we report the influence of heritability and allelic effect of the quantitative trait locus on detection of cis- and trans-acting eQTLs and discuss how these factors operate in a tissue-specific context. We identified several hundred major eQTLs in each tissue and found that cis-acting eQTLs are highly heritable and easier to detect than trans-eQTLs. The proportion of heritable expression traits was similar in all tissues; however, heritability alone was not a reliable predictor of whether an eQTL will be detected. We empirically show how the use of heritability as a filter reduces the ability to discover trans-eQTLs, particularly for eQTLs with small effects. Only 3% of cis- and trans-eQTLs exhibited large allelic effects, explaining more than 40% of the phenotypic variance, suggestive of a highly polygenic control of gene expression. Power calculations indicated that, across tissues, minor differences in genetic effects are expected to have a significant impact on detection of trans-eQTLs. Trans-eQTLs generally show smaller effects than cis-eQTLs and have a higher false discovery rate, particularly in more heterogeneous tissues, suggesting that small biological variability, likely relating to tissue composition, may influence detection of trans-eQTLs in this system. We delineate the effects of genetic architecture on variation in gene expression and show the sensitivity of this experimental design to tissue sampling variability in large-scale eQTL studies

Structural Alterations from Multiple Displacement Amplification of a Human Genome Revealed by Mate-Pair Sequencing

Comprehensive identification of the acquired mutations that cause common cancers will require genomic analyses of large sets of tumor samples. Typically, the tissue material available from tumor specimens is limited, which creates a demand for accurate template amplification. We therefore evaluated whether phi29-mediated whole genome amplification introduces false positive structural mutations by massive mate-pair sequencing of a normal human genome before and after such amplification. Multiple displacement amplification led to a decrease in clone coverage and an increase by two orders of magnitude in the prevalence of inversions, but did not increase the prevalence of translocations. While multiple strand displacement amplification may find uses in translocation analyses, it is likely that alternative amplification strategies need to be developed to meet the demands of cancer genomics

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy