Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T04:12:04.089Z Has data issue: false hasContentIssue false

11 - Spatial Modeling

from II - Predictive Modeling Methods

Published online by Cambridge University Press:  05 August 2014

By
Eike Brechmann  and
Claudia Czado
Edited by
Edward W. Frees ,
Richard A. Derrig  and
Glenn Meyers
Eike Brechmann
Affiliation:
Technische Universität München
Claudia Czado
Affiliation:
Technische Universitat in Munich
Edward W. Frees
Affiliation:
University of Wisconsin, Madison
Richard A. Derrig
Affiliation:
Temple University, Philadelphia
Glenn Meyers
Affiliation:
ISO Innovative Analytics, New Jersey
Get access

Summary

Chapter Preview. This chapter presents statistical models that can handle spatial dependence among variables. Spatial dependence refers to the phenomenon that variables observed in areas close to each other are often related. Ignoring data heterogeneity due to such spatial dependence patterns may cause overdispersion and erroneous conclusions. In an actuarial context, it is important to take spatial information into account in many cases, such as in the insurance of buildings threatened by natural catastrophes; in health insurance, where diseases affect specific regions; and also in car insurance, as we discuss in an application.

In particular, we describe the most common spatial autoregressive models and show how to build a joint model for claim severity and claim frequency of individual policies based on generalized linear models with underlying spatial dependence. The results show the importance of explicitly considering spatial information in the ratemaking methodology.

Introduction

It is important to take spatial information related to insurance policies into account when predicting claims and ratemaking. The most prominent example is the modeling of natural catastrophes needed for the insurance of buildings. Another example is health insurance, where spatial information is relevant for an accurate assessment of the underlying risks, because frequencies of some diseases may vary by region. Frequencies in neighbor regions are often expected to be more closely related than those in regions far from each other. This phenomenon is usually referred to as spatial dependence.

Type
Chapter
Information
Predictive Modeling Applications in Actuarial Science , pp. 260 - 279
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Banerjee, S., B. P., Carlin, and A. E., Gelfand (2003). Hierarchical Modeling and Analysis for Spatial Data. Chapman & Hall, London.CrossRefGoogle Scholar
Belitz, C., A., Brezger, T., Kneib, S., Lang, and N., Umlauf (2012). BayesX – Software for Bayesian inference in structured additive regression models. Version 2.1, http://www.stat.uni-muenchen.de/~bayesx.
Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, Series B 36(2), 192–236.Google Scholar
Besag, J., J., York, and A., Mollié (1991). Bayesian image restoration with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics 43(1), 1–59.CrossRefGoogle Scholar
Bivand, R. et al. (2013). spdep: Spatial dependence: weighting schemes, statistics and models. R package, http://CRAN.R-project.org/package=spdep.
Cressie, N. A. C. (1993). Statistics for Spatial Data. Wiley, New York.Google Scholar
Cressie, N. A. C. and C., Wikle (2011). Statistics for Spatio-Temporal Data. Wiley, Hoboken, NJ.Google Scholar
Czado, C. and S., Prokopenko (2008). Modelling transport mode decisions using hierarchical logistic regression models with spatial and cluster effects. Statistical Modelling 8(4), 315–345.CrossRefGoogle Scholar
Czado, C., H., Schabenberger, and V., Erhardt (2013). Non nested model selection for spatial count regression models with application to health insurance. Statistical Papers, http://dx.doi.org/10.1007/s00362012-04919.CrossRef
Dimakos, X. and A., Frigessi (2002). Bayesian premium rating with latent structure. Scandinavian Actuarial Journal 3, 162–184.Google Scholar
Fahrmeir, L., T., Kneib, S., Lang, and B., Marx (2013). Regression: Models, Methods and Applications. Springer, Berlin.CrossRefGoogle Scholar
Gelfand, A. E., P. J., Diggle, M., Fuentes, and P., Guttorp (2010). Handbook of Spatial Statistics. CRC Press, Boca Raton.CrossRefGoogle Scholar
Gneiting, T. and A. E., Raftery (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102, 359–378.CrossRefGoogle Scholar
Gschlößl, S. (2006). Hierarchical Bayesian spatial regression models with applications to non-life insurance. Ph. D. thesis, Technische Universitat Miinchen.
Gschlößl, S. and C., Czado (2007). Spatial modelling of claim frequency and claim size in non-life insurance. Scandinavian Actuarial Journal 107, 202–225.Google Scholar
Gschlößl, S. and C., Czado (2008). Modelling count data with overdispersion and spatial effects. Statistical Papers 49(3), 531–552.CrossRefGoogle Scholar
Lundberg, F. (1903). Approximerad framställning afsannollikhetsfunktionen. II. återfärsäkring af kollektivrisker. Almqvist … Wiksells Boktr, Uppsala.Google Scholar
Pettitt, A. N., I. S., Weir, and A. G., Hart (2002). A conditional autoregressive Gaussian process for irregularly spaced multivariate data with application to modelling large sets of binary data. Statistics and Computing 12, 353–367.CrossRefGoogle Scholar
Rue, H. and L., Held (2005). Gaussian Markov Random Fields: Theory and Applications. Chapman … Hall, London.CrossRefGoogle Scholar
Schabenberger, H. (2009). spatcounts: Spatial count regression. R package, http://CRAN.R-project.org/package=spatcounts.
Spiegelhalter, D. J., N. G., Best, B. P., Carlin, and A., Van Der Linde (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B 64(4), 583–639.Google Scholar
Sun, D., R. K., Tsutakawa, and P. L., Speckman (1999). Posterior distribution of hierarchical models using CAR(1) distributions. Biometrika 86, 341–350.CrossRefGoogle Scholar
Wall, M. M. (2004). A close look at the spatial structure implied by the CAR and SAR models. Journal of Statistical Planning and Inference 121, 311–324.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×