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references.bib
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@book{SPDEbook,
author={Krainski, Elias and Gómez Rubio, Virgilio and Bakka, Haakon and Lenzi, A and Castro-Camilo, Daniela and Simpson, Daniel and Lindgren, Finn and Rue, Håvard},
year={2018},
month={09},
publisher={Chapman and Hall/CRC},
pages={},
title={Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA},
doi={10.1201/9780429031892}
}
@article{Lindgren2011,
author = {Lindgren, Finn and Rue, H and Lindstr{\"{o}}m, J},
doi = {10.1111/j.1467-9868.2011.00777.x},
file = {:C$\backslash$:/Users/Humphreys{\_}J/Desktop/Sync{\_}Folder/Lindgren{\_}2011.pdf:pdf},
journal = {Journal of the Royal Statistical Society. Series B: Statistical Methodology},
keywords = {approximate bayesian inference,covariance functions,gaussian,gaussian fields,latent gaussian models,markov random fields,sparse matrices,stochastic partial differential},
pages = {423--498},
title = {{An explicit link between Gaussian fields and Gaussian Markov random field: The stochastic partial differential equations approach}},
volume = {73},
year = {2011}
}
@article{simpson2017,
ISSN = {08834237, 21688745},
URL = {http://www.jstor.org/stable/26408114},
abstract = {In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys' priors, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations.},
author = {Daniel Simpson and Håvard Rue and Andrea Riebler and Thiago G. Martins and Sigrunn H. Sørbye},
journal = {Statistical Science},
number = {1},
pages = {1--28},
publisher = {Institute of Mathematical Statistics},
title = {Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors},
volume = {32},
year = {2017}
}
@article{Fuglstad2019,
author = {Geir-Arne Fuglstad and Daniel Simpson and Finn Lindgren and Håvard Rue},
title = {Constructing Priors that Penalize the Complexity of Gaussian Random Fields},
journal = {Journal of the American Statistical Association},
volume = {114},
number = {525},
pages = {445-452},
year = {2019},
publisher = {Taylor & Francis},
doi = {10.1080/01621459.2017.1415907},
URL = {https://doi.org/10.1080/01621459.2017.1415907},
}
@article{Illian_2012,
author = {Janine B. Illian and Sigrunn H. S{\o}rbye and H{\aa}vard Rue},
title = {{A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA)}},
volume = {6},
journal = {The Annals of Applied Statistics},
number = {4},
publisher = {Institute of Mathematical Statistics},
pages = {1499 -- 1530},
keywords = {Cox processes, marked point patterns, model assessment, model comparison},
year = {2012},
doi = {10.1214/11-AOAS530},
URL = {https://doi.org/10.1214/11-AOAS530}
}
@article{Lindgren_2015,
title={Bayesian Spatial Modelling with R-INLA},
volume={63},
url={https://www.jstatsoft.org/index.php/jss/article/view/v063i19},
doi={10.18637/jss.v063.i19},
abstract={The principles behind the interface to continuous domain spatial models in the RINLA software package for R are described. The integrated nested Laplace approximation (INLA) approach proposed by Rue, Martino, and Chopin (2009) is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging from (generalized) linear mixed to spatial and spatio-temporal models. Combined with the stochastic partial differential equation approach (SPDE, Lindgren, Rue, and Lindström 2011), one can accommodate all kinds of geographically referenced data, including areal and geostatistical ones, as well as spatial point process data. The implementation interface covers stationary spatial models, non-stationary spatial models, and also spatio-temporal models, and is applicable in epidemiology, ecology, environmental risk assessment, as well as general geostatistics.},
number={19},
journal={Journal of Statistical Software},
author={Lindgren, Finn and Rue, Håvard},
year={2015},
pages={1–25}
}
@article{Rue2009,
abstract = {Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (gener- alized) additive models, smoothing spline models, state space models, semiparametric regres- sion, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models.We consider approximate Bayesian inference in a popular subset of struc- tured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables.The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis.We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its gen- erality, which makes it possible to performBayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.},
author = {Rue, H{\aa}vard and Martino, Sara and Chopin, Nicolas},
doi = {10.1111/j.1467-9868.2008.00700.x},
file = {:C\:/Users/humph173/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Rue, Martino, Chopin - 2009 - Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximat(2).pdf:pdf},
isbn = {1369-7412},
issn = {13697412},
journal = {Journal of the Royal Statistical Society. Series B: Statistical Methodology},
keywords = {Approximate Bayesian inference,Gaussian Markov random fields,Generalized additive mixed models,Laplace approximation,Parallel computing,Sparse matrices,Structured additive regression models},
mendeley-groups = {Biogeo SDM,Phyllotis,LDI,Lygodium,CitedWM,Thought/Wetland Map,GeoResearch,VSV 2014_15},
number = {2},
pages = {319--392},
title = {{Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations}},
volume = {71},
year = {2009}
}
@article{Karcher_2017,
abstract = {We introduce phylodyn, an R package for phylodynamic analysis based on gene genealogies. The package main functionality is Bayesian nonparametric estimation of effective population size fluctuations over time. Our implementation includes several Markov chain Monte Carlo-based methods and an integrated nested Laplace approximation-based approach for phylodynamic inference that have been developed in recent years. Genealogical data describe the timed ancestral relationships of individuals sampled from a population of interest. Here, individuals are assumed to be sampled at the same point in time (isochronous sampling) or at different points in time (heterochronous sampling); in addition, sampling events can be modeled with preferential sampling, which means that the intensity of sampling events is allowed to depend on the effective population size trajectory. We assume the coalescent and the sequentially Markov coalescent processes as generative models of genealogies. We include several coalescent simulation functions that are useful for testing our phylodynamics methods via simulation studies. We compare the performance and outputs of various methods implemented in phylodyn and outline their strengths and weaknesses. R package phylodyn is available at https://github.com/mdkarcher/phylodyn.},
archivePrefix = {arXiv},
arxivId = {1610.05817},
author = {Karcher, Michael D. and Palacios, Julia A. and Lan, Shiwei and Minin, Vladimir N.},
doi = {10.1111/1755-0998.12630},
eprint = {1610.05817},
file = {:C\:/Users/humph173/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Karcher et al. - 2017 - phylodyn an R package for phylodynamic simulation and inference(2).pdf:pdf},
issn = {1755098X},
journal = {Molecular Ecology},
mendeley-groups = {LGenetics,VSV 2014_15},
pages = {1--9},
title = {{phylodyn: an R package for phylodynamic simulation and inference}},
year = {2017}
}