IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v69y2020i5p1067-1090.html
   My bibliography  Save this article

Burglary in London: insights from statistical heterogeneous spatial point processes

Author

Listed:
  • Jan Povala
  • Seppo Virtanen
  • Mark Girolami

Abstract

To obtain operational insights regarding the crime of burglary in London, we consider the estimation of the effects of covariates on the intensity of spatial point patterns. Inspired by localized properties of criminal behaviour, we propose a spatial extension to mixtures of generalized linear models from the mixture modelling literature. The Bayesian model proposed is a finite mixture of Poisson generalized linear models such that each location is probabilistically assigned to one of the groups. Each group is characterized by the regression coefficients, which we subsequently use to interpret the localized effects of the covariates. By using a blocks structure of the study region, our approach enables specifying spatial dependence between nearby locations. We estimate the proposed model by using Markov chain Monte Carlo methods and we provide a Python implementation.

Suggested Citation

  • Jan Povala & Seppo Virtanen & Mark Girolami, 2020. "Burglary in London: insights from statistical heterogeneous spatial point processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1067-1090, November.
  • Handle: RePEc:bla:jorssc:v:69:y:2020:i:5:p:1067-1090
    DOI: 10.1111/rssc.12431
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssc.12431
    Download Restriction: no

    File URL: https://libkey.io/10.1111/rssc.12431?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Danilo Alvares & Carmen Armero & Anabel Forte, 2018. "What Does Objective Mean in a Dirichlet†multinomial Process?," International Statistical Review, International Statistical Institute, vol. 86(1), pages 106-118, April.
    2. Taddy, Matthew A., 2010. "Autoregressive Mixture Models for Dynamic Spatial Poisson Processes: Application to Tracking Intensity of Violent Crime," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1403-1417.
    3. repec:dau:papers:123456789/4648 is not listed on IDEAS
    4. Jesper Møller & Rasmus P. Waagepetersen, 2007. "Modern Statistics for Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 643-684, December.
    5. Carmen Fernández & Peter J. Green, 2002. "Modelling spatially correlated data via mixtures: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 805-826, October.
    6. Gelfand A.E. & Kim H-J. & Sirmans C.F. & Banerjee S., 2003. "Spatial Modeling With Spatially Varying Coefficient Processes," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 387-396, January.
    7. Green P.J. & Richardson S., 2002. "Hidden Markov Models and Disease Mapping," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1055-1070, December.
    8. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vidal Rodeiro, Carmen L. & Lawson, Andrew B., 2005. "An evaluation of the edge effects in disease map modelling," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 45-62, April.
    2. Tsionas, Mike G. & Izzeldin, Marwan & Trapani, Lorenzo, 2022. "Estimation of large dimensional time varying VARs using copulas," European Economic Review, Elsevier, vol. 141(C).
    3. Mike Tsionas & Marwan Izzeldin & Lorenzo Trapani, 2019. "Bayesian estimation of large dimensional time varying VARs using copulas," Papers 1912.12527, arXiv.org.
    4. Ranjan, Rakesh & Sen, Rijji & Upadhyay, Satyanshu K., 2021. "Bayes analysis of some important lifetime models using MCMC based approaches when the observations are left truncated and right censored," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    5. Ioannis Bournakis & Mike Tsionas, 2024. "A Non‐parametric Estimation of Productivity with Idiosyncratic and Aggregate Shocks: The Role of Research and Development (R&D) and Corporate Tax," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(3), pages 641-671, June.
    6. Chen, Zhongfei & Wanke, Peter & Tsionas, Mike G., 2018. "Assessing the strategic fit of potential M&As in Chinese banking: A novel Bayesian stochastic frontier approach," Economic Modelling, Elsevier, vol. 73(C), pages 254-263.
    7. Giuseppe Espa & Giuseppe Arbia & Diego Giuliani, 2013. "Conditional versus unconditional industrial agglomeration: disentangling spatial dependence and spatial heterogeneity in the analysis of ICT firms’ distribution in Milan," Journal of Geographical Systems, Springer, vol. 15(1), pages 31-50, January.
    8. Atkinson, Scott E. & Tsionas, Mike G., 2021. "Generalized estimation of productivity with multiple bad outputs: The importance of materials balance constraints," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1165-1186.
    9. Caroline Khan & Mike G. Tsionas, 2021. "Constraints in models of production and cost via slack-based measures," Empirical Economics, Springer, vol. 61(6), pages 3347-3374, December.
    10. Cui Guo & Jian Kang & Timothy D. Johnson, 2022. "A spatial Bayesian latent factor model for image‐on‐image regression," Biometrics, The International Biometric Society, vol. 78(1), pages 72-84, March.
    11. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model‐based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354, March.
    12. Jia Liu & John M. Maheu & Yong Song, 2024. "Identification and forecasting of bull and bear markets using multivariate returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 723-745, August.
    13. Dimitrakopoulos, Stefanos & Tsionas, Mike, 2019. "Ordinal-response GARCH models for transaction data: A forecasting exercise," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1273-1287.
    14. Michaela Prokešová & Eva Jensen, 2013. "Asymptotic Palm likelihood theory for stationary point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 387-412, April.
    15. Vanhatalo, Jarno & Veneranta, Lari & Hudd, Richard, 2012. "Species distribution modeling with Gaussian processes: A case study with the youngest stages of sea spawning whitefish (Coregonus lavaretus L. s.l.) larvae," Ecological Modelling, Elsevier, vol. 228(C), pages 49-58.
    16. Chunfang Zhao & Yingliang Wu & Yunfeng Chen & Guohua Chen, 2023. "Multiscale Effects of Hedonic Attributes on Airbnb Listing Prices Based on MGWR: A Case Study of Beijing, China," Sustainability, MDPI, vol. 15(2), pages 1-21, January.
    17. Stephen G. Hall & Heather D. Gibson & G. S. Tavlas & Mike G. Tsionas, 2020. "A Monte Carlo Study of Time Varying Coefficient (TVC) Estimation," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 115-130, June.
    18. Will Penny & Biswa Sengupta, 2016. "Annealed Importance Sampling for Neural Mass Models," PLOS Computational Biology, Public Library of Science, vol. 12(3), pages 1-25, March.
    19. Kumbhakar, Subal C. & Tsionas, Efthymios G., 2016. "The good, the bad and the technology: Endogeneity in environmental production models," Journal of Econometrics, Elsevier, vol. 190(2), pages 315-327.
    20. Spezia, L. & Cooksley, S.L. & Brewer, M.J. & Donnelly, D. & Tree, A., 2014. "Modelling species abundance in a river by Negative Binomial hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 599-614.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssc:v:69:y:2020:i:5:p:1067-1090. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.