Hierarchical dynamic spatiotemporal models; Geostatistical models
Definition
A hierarchical spatial model is the product of conditional distributions for data conditioned on a spatial process and parameters, the spatial process conditioned on the parameters defining the spatial dependencies between process locations and the parameters themselves.
Historical Background
Scientists across a wide range of disciplines have long recognized the importance of spatial dependencies in their data and the underlying process of interest. Initially due to computational limitations, they dealt with such dependencies by randomization and blocking rather than the explicit characterization of the dependencies in their models. Early developments in spatial modeling started in the 1950s and 1960s motivated by problems in mining engineering and meteorology (Cressie 1993), followed by the introduction of Markov random fields (Besag 1974). The application of hierarchical spatial and...
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Banerjee S, Gelfand AE, Finley AO, Sang H (2008) Gaussian predictive process models for large spatial data sets. J R Stat Soc: Ser B (Stat Methodol) 70:825–848. doi:10.1111/j.1467-9868.2008.00663.x
Banerjee S, Carlin BP, Gelfand AE (2015) Hierarchical modeling and analysis for spatial data, 2nd edn. CRC, Boca Raton
Berliner LM (1996) Hierarchical Bayesian time series models. In: Hanson K, Silver R (eds) Maximum entropy and Bayesian methods. Kluwer Academic, Dordrecht/Boston, pp 15–22
Besag J (1974) Spatial interactions and the statistical analysis of lattice systems (with discussion). J R Stat Soc Ser B 36:192–236
Besag J, York JC, Mollie A (1991) Bayesian image restoration, with two applications in spatial statistics (with discussion). Ann Inst Stat Math 43:1–59
Carlin BP, Banerjee S (2003) Hierarchical multivariate CAR models for saptio-temporally correlated survival data (with discussion). In: Bernardo JM, Bayarri MJ, Berger JO, Dawid AP, Heckerman D, Smith AFM, West M (eds) Bayesian statistics, vol 7. Oxford University Press, Oxford, pp 45–63
Cressie NAC (1993) Statistics for spatial data. Wiley, New York
Cressie N, Huang H-C (1999) Classes of nonseparable spatio-temporal stationary covariance functions. J Am Stat Assoc 94:1330–1340
Cressie N, Johannesson G (2008) Fixed rank kriging for very large spatial data sets. J R Stat Soc: Ser B (Stat Methodol) 70:209–226. doi:10.1111/j.1467-9868.2007.00633.x
Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, Hoboken
Diggle PJ, Tawn JA, Moyeed RA (1998) Model-based geostatistics (with discussions). Appl Stat 47(3):299–350
Givens GH, Hoeting JA (2005) Computational statistics. Wiley, Hoboken
Hanks EM, Schliep EM, Hooten MB, Hoeting JA (2015) Restricted spatial regression in practice: geostatistical models, confounding, and robustness under model misspecification. Environmetrics. doi:10.1002/env.2331
Higdon D (1998) Space and space-time modeling using process convolutions. In: Quantitative methods for current environmental issues. Springer, London, pp 37–56
Hodges JS, Reich BJ (2010) Adding spatially-correlated errors can mess up the fixed effect you love. Am Stat 64(4):325–334
Huang H-C, Cressie N (1996) Spatio-temporal prediction of snow water equivalent using the Kalman filter. Comput Stat Data Anal 22:159–175
Lindley DV, Smith AFM (1972) Bayes estimates for the linear model. J R Stat Soc Ser B 34:1–41
Paciorek CJ (2010) The importance of scale for spatial-confounding bias and precision of spatial regression estimators. Stat Sci 25(1):107–125
Rue H, Martino S, Chopin N (2009) Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J R Stat Soc Ser B 71:319–392
Stein ML (2005) Space-time covariance functions. J Am Stat Assoc 100:320–321
Waller LA, Xia BP, Gelfand AE (1997) Hierarchical spatio-temporal mapping of disease rates. J Am Stat Assoc 92:607–617
West M, Harrison J (1989) Bayesian forecasting and dynamic models. Springer, New York
Whittle P (1954) On stationary processes in the plane. Biometrika 41(3):434–449
Wikle CK (2010) Low-rank representations for spatial processes. In: Handbook of spatial statistics. pp 107–118
Wikle CK, Berliner LM (2005) Combining information across spatial scales. Technometrics 47:80–91
Wikle CK, Cressie N (1999) A dimension-reduced approach to space-time Kalman filtering. Biometrika 86(4):815–829
Wikle CK, Hooten MB (2006) Hierarchical Bayesian spatio-temporal models for population spread. In: Clark JS, Gelfand AE (eds) Hierarchical modelling for the environmental sciences. Oxford University Press, Oxford, pp 145–169
Wikle CK, Hooten MB (2010) A general science-based framework for dynamical spatio-temporal models. Test 19(3):417–451
Wikle CK, Berliner LM, Cressie N (1998) Hierarchical Bayesian space-time models. J Environ Ecol Stat 5:117–154
Wikle CK, Millif RF, Nychka D, Berliner LM (2001) Spatiotemporal hierarchical Bayesian modeling: tropical ocean surface winds. J Am Stat Assoc 96:382–397
Recommended Reading
Wikle CK (2015) Modern perspectives on statistics for spatio-temporal data. Wiley Interdiscip Rev Comput Stat 7(1):86–98
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this entry
Cite this entry
Arab, A., Hooten, M.B., Wikle, C.K. (2017). Hierarchical Spatial Models. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_564
Download citation
DOI: https://doi.org/10.1007/978-3-319-17885-1_564
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17884-4
Online ISBN: 978-3-319-17885-1
eBook Packages: Computer ScienceReference Module Computer Science and Engineering