# A Novel Non-Parametric Spatiotemporal Scan Statistic: An Application to Detect Disease Outbreaks
## 1 Introduction  
In general, scan statistics are designed and used for analyzing count data, i.e., point processes. Past literature reveals the use of several versions of spatiotemporal scan statistics in disease outbreak detection. Some of the related works are presented in [1, 2, 3, 4]. In most of these studies, scan statistics show a greater ability in detecting disease outbreak areas. However, in all these studies, it is assumed that the response variable (i.e., disease-related events) follows a Poisson distribution and thus that events are independent of each other. For instance, both the Space Time Scan Statistic and Space Time Permutation Scan Statistic assume that the number of occurrences follow a Poisson distribution. However, in reality, the occurrences of communicable diseases are not independent of each other with respect to time as well as space. For example, in the domain of disease data, it is unreasonable to assume that disease events are independent. It is highly likely that disease cases are dependent on each other based on both the location and time aspects. Hence, the use of parametric scan statistics will not always yield the correct results and might distort the real scenario.  
Given these facts, with a new perspective of clustering, the authors of [5] introduced the Mann-Whitney Scan Statistic, which allows the detection of clusters in continuous data indexed by time or by space, without any distributional assumptions or parameters to set up. This scan statistic is based on the Mann-Whitney test [6], which is used to test whether the distributions of two samples of continuous observations are equal, or at least whether their medians are equal.  
The authors of [7] suggested that the use of the non-parametric concentration index may be more powerful than likelihood ratio tests to detect cluster presence in point processes. Thus, the study [8] used the distribution-free null hypothesis, \"the marks are realizations of independent and identically distributed random variables\", in analyzing the spatially marked point processes. The same null hypothesis was used by the authors of [5] in defining the Mann-Whitney Scan Statistic but with continuous marks. The nullhypothesis used in [1; 9] is the same, but there is a specific pre-determined distribution (Bernoulli, Poisson or Gaussian).  
The methodology proposed in [5] is only focused on identifying the most significant cluster, but not the secondary clusters. However, finding secondary clusters is straightforward using the procedure proposed in [10]. This method suggests, once a significant cluster is found, to remove the data included in the significant cluster and restart the analyzing process.  
In literature, there are some studies which propose non-parametric tests, such as [11; 12]. However, these studies focus only on spatial data. The study [5] introduced the Mann-Whitney Scan Statistic either to be applied in a spatial or temporal context. The present paper introduces the Mann-Whitney Scan Statistic that can also be applied to spatiotemporal data using the spatiotemporal distance introduced in [13]. Taking this into account, the ultimate objective of this study is to extend the Mann-Whitney Scan Statistic to be applied in the spatiotemporal context.  
The next section of this paper describes the development of the Spatiotemporal Mann-Whitney Scan Statistic. Section 3 demonstrates its application to a simulated dataset and real-time application to detect COVID-19 outbreak. Furthermore, this section explicitly compares the performance of the novel Spatiotemporal Mann-Whitney Scan Statistic against the widely used parametric scan statistics in disease outbreak areas. Finally, the Section 4 presents the concluding remarks and discusses the limitations and further improvements of the study.