Data assimilation and forecasting for urban crime models

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.

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.