Data assimilation and forecasting for urban crime models

Lead Research Organisation: University of Surrey
Department Name: Mathematics

Abstract

In recent years, a great deal of research activities associated with big data analytics of crime events and crime patterns has greatly expanded and been increasingly received attentions from practitioners and government agencies; for example, "Big data, crime and security" programme run by Parliamentary Office of Science and Technology (POST) and many crime-related projects run by the Partnership for Conflict, Crime and Security Research (PaCCS). With an availability of a large amount of crime data, there is an opportunity to transform the 'Big data' into intelligence that will aid the law enforcement in switching from the incident-oriented policing toward proactive and strategic policing, which will lead to the most effective use of resources.

With the aim of understanding dynamics of crime patterns, recent mathematical research has developed several crime models such as agent-based model (ABM) for the urban burglary that incorporate well-known interactions between individual criminals and environment at the neighbourhood level. These models provide an important tool to establish the links between hypothesised criminal behaviours embedded in the models and real-world observed crime data. What is missing, however, is a novel data assimilation technique of crime data analytics that can statistically merge the model predictions with the real-world crime data in order to make better projections of future crime patterns as well as quantified the hypothesised criminal behaviour within the crime models.

The primary aim of the proposed research is to develop a practical computational tool in the framework of the sequential (Bayesian) data assimilation to statistically merge complex crime models with crime data. The research holds a promise of improving a predictive distribution of the crime rate and identifying the future of crime pattern through joint state-parameter estimation. A long-term policing strategy to reduce overall crime rate would greatly benefit from such data analytic tool. A theoretical understanding of the computational method in term of stability analysis and convergence rate will be studied to gain an insight into the applicability as well as limits of the method.

The proposed work will also address the challenges in making a prediction of crime patterns in a rapidly changing situation, reflected through a drastic change of model parameter values. This problem is difficult to overcome in the previous research where non-parametric estimation or maximum likelihood framework was employed since these methods require optimisation under a large volume of data altogether. The sequential data assimilation, however, fit naturally to this problem when appropriately designed.

The computational tool will be applied to the real-world crime data, which is accessible via the UCL-based secure data lab. With a collaboration with Prof. Shane Johnson, a criminologist at UCL, we will determine the relevance of the results to the practical use.

Planned Impact

The proposed research will impact on both research communities in academic and non-academic beneficiaries due to its inherent interdisciplinary approach that will develop a novel mathematical technique for data assimilation, focusing attention on the relevance of real-world crime pattern analysis and prediction.

In a short time-scale of 4-5 years from beginning of the proposal, we plan to significantly impact the UK scientific communities by creating new research activities in crime data analysis, to which the nonlinear filtering techniques for Poisson-process data developed in this work can be adapted or modified for various crime models. The proposed research will open an opportunity for academic beneficiaries who need to carry out a high-dimensional data assimilation and uncertainty quantification for Poisson observations. In addition, the proposal will also give a starting point to many data assimilation research groups for further development of more advanced stochastic filters for Poisson data, not only in the context of crime data assimilation but also other related areas where data enter the algorithm as a point process; for example, parameter fitting of neural spike data.

For economic and social impact, there is a potential for a practical use in providing improved short-term and long-term projections of future crime patterns such as crime hot spots, which will aid the law enforcement officers in strategic planning of crime reduction. The proposed project will also enable researchers in crime models to calibrate model parameters that will lead to improved simulation and prediction of the real-world crime patterns. The key part of the proposal will also bring together experts in pattern formation analysis and data assimilation and criminologists to gain an insight into how to provide reliable uncertainty analysis of future crime for crime reduction.

To ensure that all beneficiaries will be able to take advantage of the research programme, the PI will carry out the following activities.
1. One-day workshop (PI) : The workshop will provide an opportunity to disseminate results of the programme and engage with the UK academic communities and beneficiaries from other disciplines. It will also provide a peer knowledge exchange opportunity between practitioners and academics to fill the gap between the academic research and practical uses.
2. Website and blog (PI and Lloyd) - To stimulate interactions with a wider audience and increase outreach to beneficiaries and broaden communications among the general public, government agencies, and scientists.
3. Numerical package (PI) - To provide beneficiaries a platform for potential applications.

Publications

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Santitissadeekorn N (2020) Approximate filtering of conditional intensity process for Poisson count data: Application to urban crime in Computational Statistics & Data Analysis

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Santitissadeekorn N (2018) Sequential data assimilation for 1D self-exciting processes with application to urban crime data in Computational Statistics & Data Analysis

 
Description The proposed algorithm/tool is able to correctly quantify the near-repeat victimisation and broken-window effects, which are hypothesized in several studies of crime data.

To the best of my knowledge, we carried out the first study of how the above two effects would impact the prediction skills in the context of police patrol allocation (PPA). Our discovery demonstrates that the high degree of these effects, as quantified by our novel algorithm, can improve the prediction skill while the low degree will not make a significant improvement of a prediction based naively on the historical average (e.g. the average number of burglary over 10 years).
Exploitation Route The algorithm is used in the different applications of crime data by the world-leading research group of mathematical crime data analysis, led by Martin Short (Georgia Tech, USA).
and Jeffrey Brantingham (UCLA, USA).

Based on the results in this work, we are able to draw a collaboration with NPL researchers to test our algorithm with the land subsidence data. This leads to the IAA grants (funded by University of Surrey) to hire a 6-month postdoc position.
Sectors Communities and Social Services/Policy

Creative Economy

Environment

 
Title Influence network construction from a time-series of count data 
Description The method developed during this grant period has recently been modified for an innovative application. In particular, the new algorithm is capable to infer an influence structure for a large-scale social network based on a time-series of count data. 
Type Of Material Improvements to research infrastructure 
Year Produced 2023 
Provided To Others? Yes  
Impact This new development focuses on a feasibility of the algorithm to infer an influence structure for a large-scale network. Most existing works lack of a systematic way to construct the influence structure from a time-series of count data and scalability for a large network. Thus, the algorithm is designed to allow parallelization. The publication to demonstrate this method is published with Gold open access. 
URL https://www.sciencedirect.com/science/article/pii/S0167278923000301
 
Title Approximating filter for count data 
Description Ensemble Poisson-Gamma filter (EnPGF) and Extended Poisson-Kalman filter( ExPKF) are developed to quantify the uncertainty of the crime rate as well as the parameters used in the prescribed crime model. 
Type Of Material Computer model/algorithm 
Year Produced 2018 
Provided To Others? Yes  
Impact (1) The discovery of a way to quantify the near-repeat victimisation and broken-window effects from a big data of crime record provides insights into how the police patrol allocation (PPA) can benefit from these two effects. This led to the trials on real-world crime data, which won an award of Impact Acceleration Account Application funded by University of Surrey for 6-months period (Aug 2018-Feb 2019). The result shows that for the crime data in Chicago, PPA may not benefit much by incorporating the knowledge of near-repeat victimization and broken-window effects into their patroling strategy. (2) The original work that developed the ensemble Poisson-Gamma filter draws interest from NPL researchers in the area of subsidence data analysis for an insurance application. The collaboration with NPL researchers to test the EnPGF algorithm on the subsidence data and high-dimensional Hawkes process has won an award of Impact Acceleration Account Application funded by University of Surrey for 6-months period (Feb-July 2019) The mathematical model for subsidence has a similar self-excitation or contagious behaviour similar to the broken-window effect in crimes. Thus, the potential benefit of crime model such as Hawkes process in combination with data assimilation algorithm is promising for improving the model simulation to match with the real-world observation. The challenge is, however, the complexity of the spatiotemporal model and the information about the correlation of the process. 
 
Title Data for: Approximate Filtering of conditional intensity process for Poisson count data: application to Urban Crime 
Description Files are written in MATLAB 2018a. The files are organised in separate folders according to Sections 3, 4 and 5 in the manuscript. 
Type Of Material Database/Collection of data 
Year Produced 2020 
Provided To Others? Yes  
URL https://data.mendeley.com/datasets/w76ydc2sw7/1
 
Title Data for: Approximate Filtering of conditional intensity process for Poisson count data: application to Urban Crime 
Description Files are written in MATLAB 2018a. The files are organised in separate folders according to Sections 3, 4 and 5 in the manuscript. 
Type Of Material Database/Collection of data 
Year Produced 2020 
Provided To Others? Yes  
URL https://data.mendeley.com/datasets/w76ydc2sw7
 
Description collaboration with Dr Martin Short, Georgia Tech, USA 
Organisation Georgia Institute of Technology
Country United States 
Sector Academic/University 
PI Contribution My research team, including Dr David Lloyd (U. of Surrey), has developed a new sequential data assimilation algorithm for unsupervised parameter tracking for urban crime model.
Collaborator Contribution Dr Martin Short supports our research team with his world-leading expertise in crime modeling and provides necessary data to test the algorithm.
Impact One research manuscript has been submitted for journal publication in Computational Statistics and Data Analysis.
Start Year 2017