Skip to main content

Advertisement

SpringerLink
Log in

Multivariate Modeling of Precipitation-Induced Home Insurance Risks Using Data Depth

  • Published:
Journal of Agricultural, Biological and Environmental Statistics Aims and scope Submit manuscript

Abstract

While political debates on climate change become increasingly heated, our houses and city infrastructure continue to suffer from an increasing trend of damages due to adverse atmospheric events, from heavier-than-usual rainfalls to heat waves, droughts, and floods. Adapting our homes and critical infrastructure to sustain the effects of climate dynamics requires novel data-driven interdisciplinary approaches for efficient risk mitigation. We develop a new systematic framework based on the machinery of statistical and machine learning tools to evaluate water-related home insurance risks and quantify uncertainty due to varying climate model projections. Furthermore, we introduce the concept of data depth to the analysis of weather and climate ensembles, which remains a novel territory for statistical depth methodology as well as the field of environmental risk and ensemble forecasting in general. We illustrate the new data-driven methodology for risk analysis in application to rainfall-related home insurance in the Canadian Prairies over 2002–2011.

Supplementary materials accompanying this paper appear online.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. All the developed R codes are available through GitHub at https://github.com/coder100100/insurance.

References

  • Akbari Asanjan A, Yang T, Hsu K, Sorooshian S, Lin J, Peng Q (2018) Short-term precipitation forecast based on the persiann system and lstm recurrent neural networks. J Geophys Res Atmos 123:12543–12563

    Article  Google Scholar 

  • Allaire J, Eddelbuettel D, Golding N, Tang Y (2016) tensorflow: R Interface to TensorFlow. https://github.com/rstudio/tensorflow

  • Alonso AM, Pena D, Romo J (2003) On sieve bootstrap prediction intervals. Stat Probab Lett 65:13–20

    Article  MathSciNet  Google Scholar 

  • Awad M, Khanna R (2015) Support vector regression. In: Efficient learning machines. Springer, pp 67–80

  • Barnes C, Brierley CM, Chandler RE (2019) New approaches to postprocessing of multi-model ensemble forecasts. Q J R Meteorol Soc 145:3479–3498

    Article  Google Scholar 

  • Basak D, Pal S, Patranabis D (2007) Support vector regression. Neural Inf Process Lett Rev 11:203–224

    Google Scholar 

  • Blandino A (2021) Some Bootstrap methods for regression and time series. Ph.D. thesis. UC Davis

  • Brooks GR (2001) A synthesis of geological hazards in Canada, Bulletin 548. Technical Report, Geological Survey of Canada

    Book  Google Scholar 

  • Bühlmann P (1997) Sieve bootstrap for time series. Bernoulli 3:123–148

    Article  MathSciNet  Google Scholar 

  • Caldeira AM, Gassenferth W, Machado MAS, Santos DJ (2015) Auditing vehicles claims using neural networks. In: Procedia Computer Science 55. 3rd International Conference on Information Technology and Quantitative Management, ITQM, pp 62–71

  • Chebana F, Ouarda TB (2011) Multivariate extreme value identification using depth functions. Environmetrics 22:441–455

    Article  MathSciNet  Google Scholar 

  • Chen KY, Wang CH (2007) Support vector regression with genetic algorithms in forecasting tourism demand. Tour Manag 28:215–226. https://doi.org/10.1016/j.tourman.2005.12.018

    Article  Google Scholar 

  • Cheng CS, Li Q, Li G, Auld H (2012) Climate change and heavy rainfall-related water damage insurance claims and losses in Ontario, Canada. J Water Resour Prot 4:49–62. https://doi.org/10.4236/jwarp.2012.42007

    Article  Google Scholar 

  • Chollet F, Allaire J (2018) Deep learning with R. Manning Publications, New York

    Google Scholar 

  • Czado C, Kastenmeier R, Brechmann EC, Min A (2012) A mixed copula model for insurance claims and claim sizes. Scand Actuar J 2012:278–305

    Article  MathSciNet  Google Scholar 

  • Davison AC, Hinkley DV (1997) Bootstrap methods and their application. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Dee DP, Uppala SM, Simmons AJ et al (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137:553–597

    Article  Google Scholar 

  • Di Bernardino E, Prieur C (2018) Estimation of the multivariate conditional tail expectation for extreme risk levels: illustration on environmental data sets. Environmetrics 29:e2510

    Article  MathSciNet  Google Scholar 

  • Febrero M, Galeano P, Gonzlez-Manteiga W (2008) Outlier detection in functional data by depth measures, with application to identify abnormal nox levels. Environmetrics 19:331–345

    Article  MathSciNet  Google Scholar 

  • Frees EW, Valdez EA (1998) Understanding relationships using copulas. N Am Actuarial J 2:1–25

    Article  MathSciNet  Google Scholar 

  • Ghorbani M, Zargar G, Jazayeri-Rad H (2016) Prediction of asphaltene precipitation using support vector regression tuned with genetic algorithms. Petroleum 2:301–306. https://doi.org/10.1016/j.petlm.2016.05.006

    Article  Google Scholar 

  • Giorgi F, Gutowski WJ (2015) Regional dynamical downscaling and the cordex initiative. Annu Rev Environ Resour 40:467–490. https://doi.org/10.1146/annurev-environ-102014-021217

    Article  Google Scholar 

  • Glasserman P, Heidelberger P, Shahabuddin P (2002) Portfolio value-at-risk with heavy-tailed risk factors. Math Financ 12:239–269

    Article  MathSciNet  Google Scholar 

  • Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, New York

    Google Scholar 

  • Harrison L, Landsfeld M, Husak G, Davenport F, Shukla S, Turner W, Peterson P, Funk C (2022) Advancing early warning capabilities with chirps-compatible ncep gefs precipitation forecasts. Sci Data 9:375

    Article  Google Scholar 

  • Hastie TJ, Tibshirani RJ, Friedman JH (2009) The elements of statistical learning: data mining, inference, and prediction. Springer, New York. https://doi.org/10.1007/978-0-387-84858-7

    Article  Google Scholar 

  • Haug O, Dimakos XK, Vardal JF, Aldrin M, Meze-Hausken E (2011) Future building water loss projections posed by climate change. Scand Actuar J 1:1–20. https://doi.org/10.1080/03461230903266533

    Article  MathSciNet  Google Scholar 

  • Hoeting JA, Madigan D, Raftery AE, Volinsky CT (1999) Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors. Stat Sci 14:382–417

    Article  Google Scholar 

  • Huber J, Stuckenschmidt H (2020) Daily retail demand forecasting using machine learning with emphasis on calendric special days. Int J Forecast 36:1420–1438

    Article  Google Scholar 

  • Hyndman RJ, Shang HL (2010) Rainbow plots, bagplots, and boxplots for functional data. J Comput Graph Stat 19:29–45

    Article  MathSciNet  Google Scholar 

  • IBC (2017) Water-related damage. Technical Report, Insurance Bureau of Canada

    Google Scholar 

  • ICLR2020 ICLR (2020) International conference on learning representations. Workshop on Tackling Climate Change with Machine Learning

  • ICML (2019) International conference on machine learning. Workshop on Climate Change: How can AI help?

  • IPCC (2007) Towards new scenarios for analysis of emissions, climate change, impacts, and response strategies. Technical Report, IPCC Expert Meeting Report

    Google Scholar 

  • IPCC (2014) Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (R. K. Pachauri & L. A. Meyer (Eds.)). Technical Report. IPCC

  • Joe H (2015) Dependence modeling with copulas. Chapman and Hall/CRC, Boca Raton

    Google Scholar 

  • Kelley KH, Fontanetta LM, Heintzman M, Pereira N (2018) Artificial intelligence: implications for social inflation and insurance. Risk Manag Insur Rev 21:373–387

    Article  Google Scholar 

  • Kendall A, Gal Y (2017) What uncertainties do we need in Bayesian deep learning for computer vision?. In: Proceedings of the 31st international conference on neural information processing systems. Curran Associates Inc., Red Hook, NY, USA. pp 5580–5590

  • Kleindessner M, von Luxburg U (2017) Lens depth function and \(k\)-relative neighborhood graph: versatile tools for ordinal data analysis. J Mach Learn Res 1–52

  • Kosiorowski D, Zawadzki Z (2022) DepthProc an R package for robust exploration of multidimensional economic phenomena, arXiv preprint

  • Kramer N, Brechmann EC, Silvestrini D, Czado C (2013) Total loss estimation using copula-based regression models. Insur Math Econ 53:829–839

    Article  MathSciNet  Google Scholar 

  • Kreiss JP, Lahiri SN (2012) Bootstrap methods for time series. In: Subba Rao T, Subba Rao S, Rao C (eds) Time series analysis: methods and applications, vol 30. handbook of statistics. Elsevier, Amsterdam, pp 3–26

    Chapter  Google Scholar 

  • Krupskii P, Joe H (2019) Nonparametric estimation of multivariate tail probabilities and tail dependence coefficients. J Multivar Anal 172:147–161

    Article  MathSciNet  Google Scholar 

  • Lin P, Su S, Lee TT (2005) Support vector regression performance analysis and systematic parameter selection. In: Proceedings. 2005 IEEE international joint conference on neural networks, 2, 877–882

  • Liu RY, Parelius JM, Singh K (1999) Multivariate analysis by data depth: descriptive statistics, graphics and inference, (with discussion and a rejoinder by Liu and Singh). Ann Stat 27:783–858

    Article  Google Scholar 

  • Lorenz MO (1905) Methods of measuring the concentration of wealth. Publ Am Stat Assoc 9:209–219

    Google Scholar 

  • Lyubchich V, Gel YR (2017) Can we weather proof our insurance? Environmetrics 28:e2433. https://doi.org/10.1002/env.2433

    Article  MathSciNet  Google Scholar 

  • Lyubchich V, Kilbourne KH, Gel YR (2019) Where home insurance meets climate change: making sense of climate risk, data uncertainty, and projections. Variance 12:278–292

    Google Scholar 

  • Lyubchich V, Newlands NK, Ghahari A, Mahdi T, Gel YR (2019) Insurance risk assessment in the face of climate change: integrating data science and statistics. Wiley Interdiscip Rev Comput Stat 11:e1462. https://doi.org/10.1002/wics.1462

    Article  MathSciNet  Google Scholar 

  • Mahalanobis PC (1936) On the generalized distance in statistics. In: Proceedings of the national institute of sciences (India), pp 49–55

  • Mearns LO, et al. (2017) The NA-CORDEX dataset, version 1.0. NCAR Climate Data Gateway. https://doi.org/10.5065/D6SJ1JCH. Accessed 17 Sept 2018

  • Meyer D, Dimitriadou E, Hornik K, Weingessel A, Leisch F (2019) e1071: misc functions of the department of statistics, probability theory group (Formerly: E1071), TU Wien. https://CRAN.R-project.org/package=e1071. r package version 1.7-3

  • Mosler K (2013) Depth statistics. In: Becker C, Fried R, Kuhnt S (eds) Robustness and complex data structures. Springer, Berlin, pp 17–34

    Chapter  Google Scholar 

  • Nieto-Reyes A, Battey H (2016) A topologically valid definition of depth for functional data. Stat Sci 31:61–79

    Article  MathSciNet  Google Scholar 

  • Pascual L, Romo J, Ruiz E (2004) Bootstrap predictive inference for ARIMA processes. J Time Ser Anal 25:449–465

    Article  MathSciNet  Google Scholar 

  • Pokotylo O, Mozharovskyi P, Dyckerhoff R (2019) Depth and depth-based classification with R package ddalpha. J Stat Softw 91:1–46. https://doi.org/10.18637/jss.v091.i05

  • PSEPC (2006) Canadian disaster database version 4.4. Technical Report. Public Safety and Emergency Preparedness Canada

  • R Core Team (2022) R: a language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria. http://www.R-project.org/

  • Raftery AE, Gneiting T, Balabdaoui F, Polakowski M (2005) Using Bayesian model averaging to calibrate forecast ensembles. Mon Weather Rev 133:1155–1174. https://doi.org/10.1175/MWR2906.1

    Article  Google Scholar 

  • Rasp S, Pritchard MS, Gentine P (2018) Deep learning to represent subgrid processes in climate models. Proc Natl Acad Sci 115:9684–9689

    Article  Google Scholar 

  • Rolnick D, Donti PL, Kaack LH, Kochanski K, Lacoste A, Sankaran K, Ross AS, Milojevic-Dupont N, Jaques N, Waldman-Brown A, Luccioni AS, Maharaj T, Sherwin ED, Mukkavilli SK, Kording KP, Gomes CP, Ng AY, Hassabis D, Platt JC, Creutzig F, Chayes J, Bengio Y (2022) Tackling climate change with machine learning. ACM Comput Surv 55:1–96

    Article  Google Scholar 

  • Rousseeuw P, Struyf A (1998) Computing location depth and regression depth in higher dimensions. Stat Comput 8:193–203

    Article  Google Scholar 

  • Rousseeuw PJ, Hubert M (1999) Regression depth. J Am Stat Assoc 94:388–402. https://doi.org/10.1080/01621459.1999.10474129

    Article  MathSciNet  Google Scholar 

  • Sansom PG, Stephenson D, Bracegirdle TJ (2017) On constraining projections of future climate using observations and simulations from multiple climate models. arXiv preprint

  • Scheel I, Ferkingstad E, Frigessi A, Haug O, Hinnerichsen M, Meze-Hausken E (2013) A Bayesian hierarchical model with spatial variable selection: the effect of weather on insurance claims. J R Stat Soc Ser C (Appl Stat) 62:85–100. https://doi.org/10.1111/j.1467-9876.2012.01039.x

    Article  MathSciNet  Google Scholar 

  • Scinocca JF, Kharin VV, Jiao Y, Qian MW, Lazare M, Solheim L, Flato GM, Biner S, Desgagne M, Dugas B (2016) Coordinated global and regional climate modeling. J Clim 29:17–35. https://doi.org/10.1175/JCLI-D-15-0161.1

    Article  Google Scholar 

  • Scrucca L (2013) Ga: a package for genetic algorithms in R. J Stat Softw 53:1–37. https://doi.org/10.18637/jss.v053.i04

  • Senge R, Bösner S, Dembczyński K, Haasenritter J, Hirsch O, Donner-Banzhoff N, Hüllermeier E (2014) Reliable classification: learning classifiers that distinguish aleatoric and epistemic uncertainty. Inf Sci 255:16–29

    Article  MathSciNet  Google Scholar 

  • Serfling R (2006) Depth functions in nonparametric multivariate inference. In: Liu RY, Serfling R, Souvaine DL (eds) Data depth: robust multivariate analysis, computational geometry, and applications. American mathematical society. volume 72 of DIMACS series in discrete mathematics and theoretical computer science, pp 1–16

  • Shaker MH, Hüllermeier E (2020) Aleatoric and epistemic uncertainty with random forests. In: Berthold MR, Feelders A, Krempl G (eds) Advances in intelligent data analysis XVIII. Springer, Cham, pp 444–456

    Chapter  Google Scholar 

  • Sheffield J, Camargo SJ, Fu R, Hu Q, Jiang X, Johnson N, Karnauskas KB, Kim ST, Kinter J, Kumar S et al (2013) North American climate in cmip5 experiments. Part ii: evaluation of historical simulations of intraseasonal to decadal variability. J Clim 26:9247–9290. https://doi.org/10.1175/JCLI-D-12-00593.1

    Article  Google Scholar 

  • Shortridge J, Camp JS (2019) Addressing climate change as an emerging risk to infrastructure systems. Risk Anal 39:959–967. https://doi.org/10.1111/risa.13234

    Article  Google Scholar 

  • Sivanandam SN, Deepa SN (2008) Introduction to genetic algorithms. Springer, Berlin

    Google Scholar 

  • Sloughter JM, Gneiting T, Raftery AE (2010) Probabilistic wind speed forecasting using ensembles and Bayesian model averaging. J Am Stat Assoc 105:25–35. https://doi.org/10.1198/jasa.2009.ap08615

    Article  Google Scholar 

  • Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14:199–222

    Article  MathSciNet  Google Scholar 

  • SOA (2014) Determining the impact of climate change on insurance risk and the global community. Technical Report. American Academy of Actuaries, Society of Actuaries

  • Tay F, Cao L (2001) Application of support vector machines in financial time series forecasting. Omega 29:309–317. https://doi.org/10.1016/S0305-0483(01)00026-3

    Article  Google Scholar 

  • Thorarinsdottir TL, Scheuerer M, Heinz C (2016) Assessing the calibration of high-dimensional ensemble forecasts using rank histograms. J Comput Graph Stat 25:105–122

    Article  MathSciNet  Google Scholar 

  • Tukey JW (1975) Mathematics and the picturing of data. In: Proceedings of the international congress of mathematicians, pp 523–531

  • Vapnik V, Chervonenkis A (1974) Theory of pattern recognition. Nauka, Moscow ([in Russian])

  • Vapnik V, Golowich S, Smola A (1997) Support vector method for function approximation, regression estimation and signal processing. In: Mozer MC, Jordan M, Petsche T (eds) Advances in neural information processing systems. MIT Press. pp 281–287. https://proceedings.neurips.cc/paper/1996/file/4f284803bd0966cc24fa8683a34afc6e-Paper.pdf

  • Wu S, Akbarov A (2011) Support vector regression for warranty claim forecasting. Eur J Oper Res 213:196–204

    Article  MathSciNet  Google Scholar 

  • Yuan FC (2012) Parameters optimization using genetic algorithms in support vector regression for sales volume forecasting. Appl Math-A J Chin Univ Ser B 2012:1480–1486

    Google Scholar 

  • Zuo Y (2021) On General Notions of Depth for Regression. Stat Sci 36:142–157. https://doi.org/10.1214/20-STS767

    Article  MathSciNet  Google Scholar 

  • Zuo Y, Serfling R (2000) General notions of statistical depth function. Ann Stat 28:461–482

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Texas at El Paso, El Paso, USA

    Asim K. Dey

  2. Princeton University, Princeton, USA

    Asim K. Dey

  3. University of Maryland Center for Environmental Science, Cambridge, USA

    Vyacheslav Lyubchich

  4. National Science Foundation, Alexandria, USA

    Yulia R. Gel

Authors
  1. Asim K. Dey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vyacheslav Lyubchich
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yulia R. Gel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yulia R. Gel.

Ethics declarations

Conflict of interest

Authors have no conflicts of interests or competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 147 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dey, A.K., Lyubchich, V. & Gel, Y.R. Multivariate Modeling of Precipitation-Induced Home Insurance Risks Using Data Depth. JABES 29, 36–55 (2024). https://doi.org/10.1007/s13253-023-00554-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13253-023-00554-1

Keywords

Search

Navigation