Spatio-temporal Models Using R-INLA with Generalized Extreme Value Distribution in Hierarchical Bayes Regression

Authors(4) :-Ro'fah Nur Rachmawati, Anik Djuraidah, Anwar Fitrianto, I Made Sumertajaya

Spatio-temporal data containing information about space, time and its interaction allows researchers to describe potential geographical pattern. Bayesian method commonly used in describing spatio-temporal data is simulated based Markov Chain Monte Carlo (MCMC). However, MCMC may be extremely slow in the posterior inference simulation process and it becomes computationally unfeasible if the specified models are complex and designed hierarchically. The Integrated Nested Laplace Approximation (INLA) in R-INLA package is approximated based method and becomes a viable alternative to fundamental limitation of the expensive MCMC computation. This paper aims to model data using Bayes spatial and spatio-temporal models divided in parametric and non-parametric temporal trend specifications. We use the number of poor people as the response that fit to generalized extreme value distribution and investigate the geographical patterns among regions by adding the socioeconomics information data set in Bayes spatial model. In Bayes spatio-temporal models we conclude classical parametric temporal trend as the best model that can describe space-time interaction based on the smallest deviance criteria. All the estimation processes are performed efficiently with R-INLA resulting fast, accurate and guarantee of convergence posterior inferences compared to MCMC's convergence issues.

Authors and Affiliations

Ro'fah Nur Rachmawati
Statistics Department, School of Computer Science, Bina Nusantara University, Jakarta, Indonesia
Anik Djuraidah
Statistics Department, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Bogor, Indonesia
Anwar Fitrianto
Statistics Department, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Bogor, Indonesia
I Made Sumertajaya
Statistics Department, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Bogor, Indonesia

Areal Data, Gaussian Markov Random Field, Laplace Approximation, Random Walk

  1. S. Banarjee, B. P. Carlin and A. E. Gelfand, “Hierarchical modelling and analysis for spatial data”, 2nd ed. US: CRC Press; 2015.
  2. M. Blangiardo and M. Cameletti, “Spatial and spatio-temporal Bayesian models with R-INLA”, 1st ed. UK: John Wiley & Sons; 2015.
  3. J. R. P. D. Carvalho, M. N. Alan and E. B. A. M. José. 2016. Spatio-temporal modeling of data imputation for daily rainfall series in homogeneous zones. Revista Brasileira de Meteorologia. 31(2):196-201. DOI: 10.1590/0102-778631220150025.
  4. J. C. Aravena and B. H. Luckman. 2009. Spatio-temporal rainfall patterns in southern south america. International Journal of Climatology. 29(14):2106-2120. DOI: 10.1002/joc.1761.
  5. J. D. Yanosky, C. J. Paciorek, F. Laden, J. E. Hart, R. C. Puett, D. Liao and H. H. Suh. 2014. Spatio-temporal modeling of particulate air pollution in the conterminous United States using geographic and meteorological predictors. Environmental Health. 13(63). DOI: 10.1186/1476-069X-13-63.
  6. R. Ye, K. Shan, H. Gao, R. Zhang, W. Xiaong, Y. Wang and X. Qian. 2014. Spatio-temporal distribution patterns in environmental factors, chlorophyll-a and microcystins in a large shallow lake. International Journal of Environmental Research and Public Health. 11(5):5155-69. DOI: 10.3390/ijerph110505155.
  7. J. J. Abellan, S. Richardson and N. Best. 2008. Use of space-time models to investigate thestability of patterns of disease. Environmental Health Perspective. 116(8):1111–9. DOI: 10.1289/ehp.10814.
  8. Z. Ma, X. Hu, A. M. Sayer, R. Levy, Q. Zhang, Y. Xue, S. Tong, J. Bi, L. Huang L and Y. Liu. 2016. Satellite-based spatiotemporal trends in PM2.5 concentrations: china, 2004–2013. Environmental Health Perspectives. 124(2):184-92. DOI: 10.1289/ehp.1409481.
  9. U. Dieckman, T. Herben and R. Law. 1999. Spatio-temporal processes in ecological communities. CWI Quarterly. 12(3&4):213 – 38.
  10. F. I. Korennoy, V. M. Gulekin, J. B. Malone, Cn. Mores, S. A. Dudnikov and M. A. Stevenson. 2014. Spatio-temporal modeling of the African swine fever epidemic in the Russian Federation, 2007–2012. Spatial and Spatio-temporal Epidemiology. 11: 135-41. DOI: 10.1016/j.sste.2014.04.002.
  11. M. Nazia, M. Ali, Md. Jakariya, Q. Nahar, M. Yunus and M. Emch. 2018. Spatial and population drivers of persistent cholera transmission in rural Bangladesh: Implications for vaccine and intervention targeting. Spatial and Spatio-temporal Epidemiology. 24: 1–9. DOI: 10.1016/j.sste.2017.09.001.
  12. D. Kaplan, “Bayesian Statistics for the Social Sciences”, 1st ed. New York: The Guilford Press; 2014.
  13. S. Jackman, “Bayesian Analysis for the Social Sciences”, 1st ed. United Kingdom: Wiley; 2009.
  14. G. Baio, A. Berardi and A. Heath, “Bayesian Cost-Effectiveness Analysis with the R package BCEA”, 1st ed. Switzerland: Springer International Publishing; 2017.
  15. M. Pirani, J. Gulliver, G. W. Fuller and M. Blangiardo. 2014. Bayesian spatiotemporal modelling for the assessment of short-term exposure to particle pollution in urban areas. Journal of Exposure Science and Environmental Epidemiology. 24: 319–27. oi:10.1038/jes.2013.85.
  16. G. Casella and E. George. 1992. Explaining the Gibbs sampler. The American Statistician. 46(3): 167–74.
  17. W. Gilks, S. Richardson and D Spiegelhalter, “Markov Chain Monte Carlo in Practice”, 1st ed. Florida: Chapman & Hall/CRC; 1996.
  18. J. Besag, J. York and A. Mollie. 1991. Bayesian image restoration, with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics. 43(1): 1–59.
  19. S. Banerjee., B. Carlin and A. Gelfand, “Hierarchical modeling and analysis for spatial data”, 2nd Ed. US: CRC Press. 2015.
  20. P. Diggle and J. P. Ribeiro, “Model-based Geostatistics”, 1st ed. New York: Springer-Verlag; 2007.
  21. N. Cressie and C. Wikle, “Statistics for spatio-temporal data”, 1st ed. New Jersey: Wiley; 2011.
  22. I. Ntzoufras, “Bayesian modeling using WinBUGS”, 1st ed. United States: John Wiley and Sons; 2009.
  23. H. Rue, S. Martino and N. Chopin. 2009. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of Royal Statistical Society B. 71(2):1–35.
  24. S. Martin and H. 2010. Rue. Implementing approximate bayesian inference using integrated nested laplace approximation: a manual for the inla program. Available from: http://www.math.ntnu.no/hrue/ GMRFsim/manual.pdf.
  25. R. Ruiz-Cárdenas, E. Krainski and H. Rue. 2012. Direct fitting of dynamic models using integrated nested laplace approximations INLA. Computational Statistics & Data Analysis. 56(6):1808–28.
  26. S. Martino, K. Aas, O. Lindqvist, L. Neef and H. Rue. 2011. Estimating stochastic volatility models using integrated nested laplace approximations. The Europian Journal of Finance 17(7):487–503. DOI: 10.1080/1351847X.2010.495475.
  27. D. Simpson, J. B. Illian, F. Lindgren, S. H. Sørbye SH and H. Rue. 2016. Going off grid: computationally efficient inference for log-Gaussian Cox processes. Biometrika. 1–22. DOI: 10.1093/biomet/asv064.
  28. A. Cosandey-Godi, E. T. Krainski, B. Worm anf J. M. Flemming. 2015. Applying Bayesian spatiotemporal models to fisheries bycatch in the Canadian Arctic. Canadian Journal of Fisheris and Aquatic Science. 72(2): 1–12. DOI.org/10.1139/cjfas-2014-0159.
  29. M. Cameletti, F. Lindgren, D. Simpson and H. Rue. 2013. Spatio-temporal modeling of particulate matter concentration through the SPDE approach. Advances in Statistical Analysis. 97(2): 109–31.
  30. A. L. Papiola, A. Riebler, A. Amaral-Turkman, R. São-João, C. Ribeiro, C. Geraldes and A. Miranda. 2013. Stomach cancer incidence in Southern Portugal 1998-2006: a spatio-temporal analysis. Biometrical Journal. 56(3):403-15. DOI: 10.1002/bimj.201200264.
  31. B. Mahmoudian and M. Mohammadzadeh. 2014. A spatio-temporal dynamic regression model for extreme wind speeds. Extremes. 17(2):221–45.
  32. S. Ghosh and B. K. Mallick. 2011. A hierarchical Bayesian spatio-temporal model for extreme precipitation events. Environmetrics. Research Article: Wiley Online Library. 22(2):192-204. DOI: 10.1002/env.1043.
  33. S. Pindado, C. Pindado C and J. Cubas J. 2017. Fréchet distribution applied to salary incomes in Spain from 1999 to 2014. An engineering approach to changes in salaries’ distribution. Economies. 2017; 5(2): 14. DOI:10.3390/economies5020014.
  34. R. A. Fisher and L. H. C. Tippett. 1928. Limiting forms of the frequency distributions of the largest or smallest member of a sample. Proceedings of the Cambridge Philosophical Society. 24(2):180-90. DOI: 10.1017/S0305004100015681.
  35. H. Rue H and L. Held, “Gaussian Markov random fields”, Theory and applications. Chapman & Hall; 2005.
  36. J. Besag. 1974. Spatial interaction and the statistical analysis of lattice systems (with discussion). Journal of Royal Statistical Society, Series B. 36(2):192–236.
  37. C. Herrmann, S. Ess1, B. Thürlimann, N. Probst-Hensch and P. Vounatsou. 2015. 40 years of progress in female cancer death risk: a Bayesian spatio-temporal mapping analysis in Switzerland. BMC Cancer. 15:666-675. DOI: 10.1186/s12885-015-1660-8.
  38. T. Gneiting T, M. G. Genton and P. Guttorp, “Statistical methods for spatio-temporal systems”, Edited by Finkenstädt B, Held L, Isham V, in Statistical Methods for Spatio-temporal Systems. CRC Press, Chapmann and Hall; 2006:151–75.
  39. D. Clayton, “Generalised linear mixed models”, Edited by Gilks W, Richardson S, Spiegelhalter D in Markov Chain Monte Carlo in Practice. Chapman & Hall; 1996:275–301.
  40. L. Knorr-Held. 2000. Bayesian modelling of inseparable space-time variation in disease risk. Statistics in Medicine. 19(17–18):2555–67.
  41. L. Bernardinelli, D. Clayton, C. Pascutto, C. Montomoli, M. Ghislandi and M. Songini. 1995. Bayesian analysis of space-time variation in disease risk. Statistics in Medicine. 14(21–22):2433–43.
  42. http://www.r-inla.org

Publication Details

Published in : Volume 4 | Issue 4 | March-April 2018
Date of Publication : 2018-04-30
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 1129-1143
Manuscript Number : IJSRSET1844338
Publisher : Technoscience Academy

Print ISSN : 2395-1990, Online ISSN : 2394-4099

Cite This Article :

Ro'fah Nur Rachmawati, Anik Djuraidah, Anwar Fitrianto, I Made Sumertajaya, " Spatio-temporal Models Using R-INLA with Generalized Extreme Value Distribution in Hierarchical Bayes Regression, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 4, Issue 4, pp.1129-1143, March-April-2018. Citation Detection and Elimination     |     
Journal URL : https://ijsrset.com/IJSRSET1844338

Article Preview