References

Asar, Özgür, David Bolin, Peter J. Diggle, and Jonas Wallin. 2020. “Linear Mixed Effects Models for Non-Gaussian Continuous Repeated Measurement Data.” Journal of the Royal Statistical Society: Series C (Applied Statistics) 69 (5): 1015–65. https://doi.org/doi.org/10.1111/rssc.12405.

Barndorff-Nielsen, Ole E, Thomas Mikosch, and Sidney I Resnick. 2012. Lévy Processes: Theory and Applications. Springer Science & Business Media.

Betancourt, Michael. 2018. “Fitting the Cauchy.” https://github.com/betanalpha/knitr_case_studies/tree/master/fitting_the_cauchy.

———. 2020. “Robust Gaussian Processes in Stan.” https://github.com/betanalpha/knitr_case_studies/tree/master/gaussian_processes.

Betancourt, Michael, and Mark Girolami. 2015. “Hamiltonian Monte Carlo for Hierarchical Models.” Current Trends in Bayesian Methodology with Applications 79 (30): 2–4.

Bolin, David. 2014. “Spatial Matérn Fields Driven by Non-Gaussian Noise.” Scandinavian Journal of Statistics 41 (3): 557–79.

Bolin, David, and Jonas Wallin. 2020. “Multivariate Type g Matérn Stochastic Partial Differential Equation Random Fields.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 82 (1): 215–39.

Cabral, Rafael, David Bolin, and Håvard Rue. 2022. “Controlling the Flexibility of Non-Gaussian Processes Through Shrinkage Priors.” arXiv Preprint arXiv:2203.05510.

Dhull, Monika Singh, and Arun Kumar. 2021. “Normal Inverse Gaussian Autoregressive Model Using EM Algorithm.” arXiv Preprint arXiv:2105.14502.

Fuglstad, Geir-Arne, Daniel Simpson, Finn Lindgren, and Håvard Rue. 2019. “Constructing Priors That Penalize the Complexity of Gaussian Random Fields.” Journal of the American Statistical Association 114 (525): 445–52.

Hooten, Mevin, Jay Ver Hoef, and Ephraim Hanks. 2019. “Simultaneous Autoregressive (SAR) Model,” November, 1–10. https://doi.org/10.1002/9781118445112.stat08208.

Ken-Iti, Sato. 1999. Lévy Processes and Infinitely Divisible Distributions. Cambridge university press.

Lindgren, Finn, Håvard Rue, and Johan Lindström. 2011. “An Explicit Link Between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73 (4): 423–98.

Matérn, Bertil. 1960. Spatial Variation: Stochastic Models and Their Application to Some Problems in Forest Surveys and Other Sampling Investigations. Statens Skogsforskningsinstitut, Stockholm.

Morris, Mitzi. 2019. “Spatial Models in Stan: Intrinsic Auto-Regressive Models for Areal Data.” https://mc-stan.org/users/documentation/case-studies/icar_stan.html.

Riebler, Andrea, Sigrunn H Sørbye, Daniel Simpson, and Håvard Rue. 2016. “An Intuitive Bayesian Spatial Model for Disease Mapping That Accounts for Scaling.” Statistical Methods in Medical Research 25 (4): 1145–65.

Rue, Håvard, and Leonhard Held. 2005. Gaussian Markov Random Fields: Theory and Applications. CRC press.

Rue, Håvard, Sara Martino, and Nicolas Chopin. 2009. “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations.” Journal of the Royal Statistical Society: Series b (Statistical Methodology) 71 (2): 319–92.

Simpson, Daniel, Håvard Rue, Andrea Riebler, Thiago G Martins, and Sigrunn H Sørbye. 2017. “Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors.” Statistical Science, 1–28.

Sørbye, Sigrunn Holbek, and Håvard Rue. 2017. “Penalised Complexity Priors for Stationary Autoregressive Processes.” Journal of Time Series Analysis 38 (6): 923–35. https://doi.org/https://doi.org/10.1111/jtsa.12242.

Team, Stan Development. 2020. “Stan Modeling Language Users Guide and Reference Manual, 2.28.” http://mc-stan.org/.

Vehtari, Aki, Andrew Gelman, and Jonah Gabry. 2017. “Practical Bayesian Model Evaluation Using Leave-One-Out Cross-Validation and WAIC.” Statistics and Computing 27 (5): 1413–32.

Ver Hoef, Jay M, Ephraim M Hanks, and Mevin B Hooten. 2018. “On the Relationship Between Conditional (CAR) and Simultaneous (SAR) Autoregressive Models.” Spatial Statistics 25: 68–85.

Walder, Adam, and Ephraim M Hanks. 2020. “Bayesian Analysis of Spatial Generalized Linear Mixed Models with Laplace Moving Average Random Fields.” Computational Statistics & Data Analysis 144: 106861.