IDEAS home Printed from https://ideas.repec.org/a/bla/jorssa/v184y2021i4p1220-1244.html
   My bibliography  Save this article

Spatio‐temporal mixed membership models for criminal activity

Author

Listed:
  • Seppo Virtanen
  • Mark Girolami

Abstract

We suggest a probabilistic approach to study crime data in London and highlight the benefits of defining a statistical joint crime distribution model which provides insights into urban criminal activity. This is achieved by developing a hierarchical mixture model for observations, crime occurrences over a geographical study area, that are grouped according to multiple time stamps and crime categories. The mixture components correspond to spatial crime distributions over the study area and the goal is to infer, based on the observations, how and to what degree the latent distributions are shared across the groups.

Suggested Citation

  • Seppo Virtanen & Mark Girolami, 2021. "Spatio‐temporal mixed membership models for criminal activity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1220-1244, October.
    • Handle: RePEc:bla:jorssa:v:184:y:2021:i:4:p:1220-1244
    DOI: 10.1111/rssa.12642
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssa.12642
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssa.12642?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. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    2. Quick, Matthew & Li, Guangquan & Brunton-Smith, Ian, 2018. "Crime-general and crime-specific spatial patterns: A multivariate spatial analysis of four crime types at the small-area scale," Journal of Criminal Justice, Elsevier, vol. 58(C), pages 22-32.
    3. Mohler, G. O. & Short, M. B. & Brantingham, P. J. & Schoenberg, F. P. & Tita, G. E., 2011. "Self-Exciting Point Process Modeling of Crime," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 100-108.
    4. Mohler, George, 2014. "Marked point process hotspot maps for homicide and gun crime prediction in Chicago," International Journal of Forecasting, Elsevier, vol. 30(3), pages 491-497.
    5. 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.
    6. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    7. Eric Piza & Shun Feng & Leslie Kennedy & Joel Caplan, 2017. "Place-based correlates of Motor Vehicle Theft and Recovery: Measuring spatial influence across neighbourhood context," Urban Studies, Urban Studies Journal Limited, vol. 54(13), pages 2998-3021, October.
    8. Chamberlain, Alyssa W. & Hipp, John R., 2015. "It's all relative: Concentrated disadvantage within and across neighborhoods and communities, and the consequences for neighborhood crime," Journal of Criminal Justice, Elsevier, vol. 43(6), pages 431-443.
    9. Liu, Hua & Brown, Donald E., 2003. "Criminal incident prediction using a point-pattern-based density model," International Journal of Forecasting, Elsevier, vol. 19(4), pages 603-622.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiao‐Li Meng, 2021. "Enhancing (publications on) data quality: Deeper data minding and fuller data confession," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1161-1175, October.

    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. Mohler, George & Carter, Jeremy & Raje, Rajeev, 2018. "Improving social harm indices with a modulated Hawkes process," International Journal of Forecasting, Elsevier, vol. 34(3), pages 431-439.
    2. Zhengyi Zhou & David S. Matteson & Dawn B. Woodard & Shane G. Henderson & Athanasios C. Micheas, 2015. "A Spatio-Temporal Point Process Model for Ambulance Demand," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 6-15, March.
    3. Ying C. MacNab, 2018. "Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 497-541, September.
    4. Jonathan Wakefield & Taylor Okonek & Jon Pedersen, 2020. "Small Area Estimation for Disease Prevalence Mapping," International Statistical Review, International Statistical Institute, vol. 88(2), pages 398-418, August.
    5. Mohler, George, 2014. "Marked point process hotspot maps for homicide and gun crime prediction in Chicago," International Journal of Forecasting, Elsevier, vol. 30(3), pages 491-497.
    6. Márcio Poletti Laurini, 2017. "A spatial error model with continuous random effects and an application to growth convergence," Journal of Geographical Systems, Springer, vol. 19(4), pages 371-398, October.
    7. Klein, Nadja & Herwartz, Helmut & Kneib, Thomas, 2020. "Modelling regional patterns of inefficiency: A Bayesian approach to geoadditive panel stochastic frontier analysis with an application to cereal production in England and Wales," Journal of Econometrics, Elsevier, vol. 214(2), pages 513-539.
    8. Amanda S. Hering & Sean Bair, 2014. "Characterizing spatial and chronological target selection of serial offenders," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 123-140, January.
    9. Santitissadeekorn, N. & Short, M.B. & Lloyd, D.J.B., 2018. "Sequential data assimilation for 1D self-exciting processes with application to urban crime data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 163-183.
    10. Peter A. Gao & Jonathan Wakefield, 2023. "A Spatial Variance‐Smoothing Area Level Model for Small Area Estimation of Demographic Rates," International Statistical Review, International Statistical Institute, vol. 91(3), pages 493-510, December.
    11. Marc Francke & Alex Van de Minne, 2021. "Modeling unobserved heterogeneity in hedonic price models," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 49(4), pages 1315-1339, December.
    12. Chen, Yewen & Chang, Xiaohui & Luo, Fangzhi & Huang, Hui, 2023. "Additive dynamic models for correcting numerical model outputs," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    13. Miriam Marco & Enrique Gracia & Antonio López-Quílez & Marisol Lila, 2021. "The Spatial Overlap of Police Calls Reporting Street-Level and Behind-Closed-Doors Crime: A Bayesian Modeling Approach," IJERPH, MDPI, vol. 18(10), pages 1-14, May.
    14. Ying C. MacNab, 2018. "Rejoinder on: Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 554-569, September.
    15. Ranjita Pandey & Himanshu Tolani, 2022. "Crime patterns in Delhi: a Bayesian spatio-temporal assessment," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(6), pages 2971-2980, December.
    16. Quick, Matthew & Li, Guangquan & Brunton-Smith, Ian, 2018. "Crime-general and crime-specific spatial patterns: A multivariate spatial analysis of four crime types at the small-area scale," Journal of Criminal Justice, Elsevier, vol. 58(C), pages 22-32.
    17. Ying C. MacNab, 2023. "On coregionalized multivariate Gaussian Markov random fields: construction, parameterization, and Bayesian estimation and inference," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 263-293, March.
    18. Osafu Augustine Egbon & Omodolapo Somo-Aina & Ezra Gayawan, 2021. "Spatial Weighted Analysis of Malnutrition Among Children in Nigeria: A Bayesian Approach," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 495-523, December.
    19. Kajita, Mami & Kajita, Seiji, 2020. "Crime prediction by data-driven Green’s function method," International Journal of Forecasting, Elsevier, vol. 36(2), pages 480-488.
    20. Rummens, Anneleen & Hardyns, Wim, 2021. "The effect of spatiotemporal resolution on predictive policing model performance," International Journal of Forecasting, Elsevier, vol. 37(1), pages 125-133.

    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:jorssa:v:184:y:2021:i:4:p:1220-1244. 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.