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

Krainski, Elias Teixeira; Gómez‐Rubio, Virgilio; Bakka, Haakon; Lenzi, Amanda; Castro‐Camilo, Daniela; Simpson, Daniel; Lindgren, Finn; Rue, Håvard

doi:10.1201/9780429031892

Cited by 196 publications

(249 citation statements)

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“…, Krainski et al. ) for R statistical computing software (version 3.3.1, R Core Team ). For parameters α i , ε i , and τ i , with CAR structure, precision matrices were scaled such that the geometric mean of marginal variances was equal to one (Sørbye and Rue , Riebler et al.…”

Section: Methodsmentioning

confidence: 99%

“…In contrast to previous work, effort and year effects were modeled as random slopes with spatial structure, following a spatially varying coefficient (SVC) approach (Gelfand et al 2003, Finley 2011, Congdon 2014). Finally, unlike prior studies using MCMC, we used integrated nested Laplace approximation (INLA) to estimate Bayesian posteriors for model parameters (Rue et al 2009, Martins et al 2013, Lindgren and Rue 2015, Blangiardo and Cameletti 2015, Bakka et al 2018, Krainski et al 2018, which led to a dramatic decrease in computing time. Our objective in developing this technique was to estimate longterm population trends at a spatial scale appropriate for evaluating ecological drivers and informing conservation actions.…”

Section: Previous Work Bymentioning

confidence: 99%

“…The SVC model described above was analyzed within a Bayesian framework using the R-INLA package (version 18.10.09, Martins et al 2013, Lindgren and Rue 2015, Blangiardo and Cameletti 2015, Bakka et al 2018, Krainski et al 2018) for R statistical computing software (version 3.3.1, R Core Team 2016). For parameters a i , e i , and s i , with CAR structure, precision matrices were scaled such that the geometric mean of marginal variances was equal to one (Sørbye and Rue 2014, Riebler et al 2016, Freni-Sterrantino et al 2018, and priors for precision parameters were penalized complexity (PC) priors, with parameter values U PC = 1 and a PC = 0.01 .…”

Section: Model Computationmentioning

confidence: 99%

“…, Krainski et al. ), which led to a dramatic decrease in computing time. Our objective in developing this technique was to estimate long‐term population trends at a spatial scale appropriate for evaluating ecological drivers and informing conservation actions.…”

Section: Introductionmentioning

confidence: 99%

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Spatial modeling of Audubon Christmas Bird Counts reveals fine‐scale patterns and drivers of relative abundance trends

2019

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Bird counts by community volunteers provide valuable information about the conservation needs of many bird species. The statistical modeling techniques commonly used to analyze these counts provide robust, long‐term population trend estimates from heterogeneous community science data at regional, national, and continental scales. Here, we present a new modeling approach that increases the spatial resolution of trend estimates and reduces the computational burden of trend estimation, each by an order of magnitude. We demonstrate the approach with data for the American Robin (Turdus migratorius) from Audubon Christmas Bird Counts conducted between 1966 and 2017. We show that aggregate regional trend estimates from the proposed method aligned well with those from the current standard method, and that spatial variation in trends was associated with winter temperatures and human population densities as predicted by ecological energetics. This technique can provide reasonable large‐scale trend estimates for users interested in general patterns, while also providing higher‐resolution estimates for examining correlates of abundance trends at finer spatial scales, which is a prerequisite for tailoring management plans to local conditions.

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Section: Methodsmentioning

confidence: 99%

Section: Previous Work Bymentioning

confidence: 99%

Section: Model Computationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spatial modeling of Audubon Christmas Bird Counts reveals fine‐scale patterns and drivers of relative abundance trends

2019

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“…Prior distributions for the hyper-parameters are specified through additional arguments. Several tools to manipulate models and likelihoods exist as described in tutorials at www.r-inla.org and the books by Blangiardo and Cameletti (2015), and Krainski et al (2018). In the supplementary section, we have included a script showing how the data was simulated from the haplotype network model and how we fitted the model to the simulated data.…”

Section: Inferencementioning

confidence: 99%

Hierarchical modeling of haplotype effects based on a phylogeny

Selle

Steinsland

Lindgren³

et al. 2020

Preprint

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This paper introduces a hierarchical model to estimate haplotype effects based on phylogenetic relationships between haplotypes and their association with observed phenotypes. In a population there are usually many, but not all possible, distinct haplotypes and few observations per haplotype. Further, haplotype frequencies tend to vary substantially -few haplotypes have high frequency and many haplotypes have low frequency. Such data structure challenge estimation of haplotype effects. However, haplotypes often differ only due to few mutations and leveraging these similarities can improve the estimation of haplotype effects. There is extensive literature on this topic. Here we build on these observations and develop an autoregressive model of order one that hierarchically models haplotype effects by leveraging phylogenetic relationships between the haplotypes described with a directed acyclic graph. The phylogenetic relationships can be either in a form of a tree or a network and we therefore refer to the model as the haplotype network model. The haplotype network model can be included as a component in a phenotype model to estimate associations between haplotypes and phenotypes. The key contribution of this work is that by leveraging the haplotype network structure we obtain a sparse model and by using hierarchical autoregression the flow of information between similar haplotypes is estimated from the data. We show with a simulation study that the hierarchical model can improve estimates of haplotype effects compared to an independent haplotype model, especially when there are few observations for a specific haplotype.We also compared it to a mutation model and observed comparable performance, though the haplotype model has the potential to capture background specific effects. We demonstrate the model with a case study of modeling the effect of mitochondrial haplotypes on milk yield in cattle.

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Statistical models of yield in on‐farm precision experimentation

et al. 2021

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On-farm precision experimentation (OFPE) is increasingly conducted using variablerate technology and precision agriculture (PA) equipment to measure the effect of changes in input application rates on yields and profits at specific fields. Classical linear regression models and new Bayesian and machine learning regressions for spatial data can be used to investigate site-specific crop response from georeferenced data. The objective of this work was to compare statistical models that can be used by researchers analyzing OFPE data to estimate crop response and better describe its spatial within-field variability. Three statistical models estimating the responses to N rates, seed rates, and site-specific soil properties from eight OFPEs were compared:(a) linear regression (LR) for spatially correlated errors, (b) Bayesian regression (BR) with random site effects, and (c) random forest regression (RF) with kriged residuals. Models were adjusted to account for spatial variation in yield response, and with and without field characteristic covariates. Modeling spatial correlation and including plot covariates improved yield predictions. Differences among methods proved to be indistinguishable with respect to average explained variance, correlation between predicted and observed values, and mean square prediction errors (PEs).However, BR and RF outperformed LR in site-specific prediction accuracy, with BR predictions having lower predictive uncertainty than RF predictions. The hierarchical Bayesian model for spatial data is a useful tool to process OFPE data, allowing direct derivation of linear coefficients and prediction uncertainty measures related to site-specific yield responses.

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

Cited by 196 publications

References 0 publications

Spatial modeling of Audubon Christmas Bird Counts reveals fine‐scale patterns and drivers of relative abundance trends

Spatial modeling of Audubon Christmas Bird Counts reveals fine‐scale patterns and drivers of relative abundance trends

Hierarchical modeling of haplotype effects based on a phylogeny

Statistical models of yield in on‐farm precision experimentation

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