Parallel Selected Inversion for Space-Time Gaussian Markov Random Fields

Performing a Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances. Although direct matrix factorizations can be used for the inversion, such methods fail to scale well for distributed problems when run on large computing clusters. On the contrary, Krylov subspace methods for the selected inversion have been gaining traction. We propose a parallel hybrid approach based on domain decomposition, which extends the Rao-Blackwellized Monte Carlo estimator for distributed precision matrices. Our approach exploits the strength of Krylov subspace methods as global solvers and efficiency of direct factorizations as base case solvers to compute the marginal variances using a divide-and-conquer strategy. By introducing subdomain overlaps, one can achieve a greater accuracy at an increased computational effort with little to no additional communication. We demonstrate the speed improvements on both simulated models and a massive US daily temperature data.Comment: 17 pages, 7 figure

Flexible modelling of spatial variation in agricultural field trials with the R package INLA

The objective of this paper was to fit different established spatial models for analysing agricultural field trials using the open-source R package INLA. Spatial variation is common in field trials, and accounting for it increases the accuracy of estimated genetic effects. However, this is still hindered by the lack of available software implementations. We compare some established spatial models and show possibilities for flexible modelling with respect to field trial design and joint modelling over multiple years and locations. We use a Bayesian framework and for statistical inference the integrated nested Laplace approximations (INLA) implemented in the R package INLA. The spatial models we use are the well-known independent row and column effects, separable first-order autoregressive ( AR1⊗AR1 ) models and a Gaussian random field (Matérn) model that is approximated via the stochastic partial differential equation approach. The Matérn model can accommodate flexible field trial designs and yields interpretable parameters. We test the models in a simulation study imitating a wheat breeding programme with different levels of spatial variation, with and without genome-wide markers and with combining data over two locations, modelling spatial and genetic effects jointly. The results show comparable predictive performance for both the AR1⊗AR1 and the Matérn models. We also present an example of fitting the models to a real wheat breeding data and simulated tree breeding data with the Nelder wheel design to show the flexibility of the Matérn model and the R package INLA

Global and Polynomial-Time Convergence of an Infeasible-Interior-Point Algorithm Using Inexact Computation(Continuous and Discrete Mathematical Optimization)

Social learning can be fundamental to cohesive group living, and schooling fishes have proven ideal test subjects for recent work in this field. For many species, both demographic factors, and inter- (and intra-) generational information exchange are considered vital ingredients in how movement decisions are reached. Yet key information is often missing on the spatial outcomes of such decisions, and questions concerning how migratory traditions are influenced by collective memory, density-dependent and density-independent processes remain open. To explore these issues, we focused on Atlantic herring (Clupea harengus), a long-lived, dense-schooling species of high commercial importance, noted for its unpredictable shifts in winter distribution, and developed a series of Bayesian space-time occurrence models to investigate wintering dynamics over 23 years, using point-referenced fishery and survey records from Icelandic waters. We included covariates reflecting local-scale environmental factors, temporally-lagged prey biomass and recent fishing activity, and through an index capturing distributional persistence over time, derived two proxies for spatial memory of past wintering sites. The previous winter's occurrence pattern was a strong predictor of the present pattern, its influence increasing with adult population size. Although the mechanistic underpinnings of this result remain uncertain, we suggest that a ‘wisdom of the crowd’ dynamic may be at play, by which navigational accuracy towards traditional wintering sites improves in larger and/or denser, better synchronized schools. Wintering herring also preferred warmer, fresher, moderately stratified waters of lower velocity, close to hotspots of summer zooplankton biomass, our results indicative of heightened environmental sensitivity in younger cohorts. Incorporating spatiotemporal correlation structure and time-varying regression coefficients improved model performance, and validation tests on independent observations one-year ahead illustrate the potential of uniting demographic information and non-stationary models to quantify both the strength of collective memory in animal groups and its relevance for the spatial management of populations

Advanced Spatial Modeling With Stochastic Partial Differential Equations Using R and INLA

No abstract available

Spatial similarity index

This folder contains R code and data to calculate the spatial similarity index (SSI), and to compute and map the ‘distrib(t)’ and ‘counts(t)’ variables, as described in Appendix 2 of the paper. See the README file for further information and file descriptions

Space time models

This folder contains R code and data to run all models described in the paper, in addition to model output for plotting Figures. 3-5, A7 and reproducing Tables 2, 3, A1-A3. See the README file for further information and file descriptions