In disease mapping, the spatial scan statistic is used to detect spatial regions where population is exposed to a significantly higher disease risk than expected. In this important application, the current residence is typically used to define the location of individuals from the population. Considering the mobility of humans at various temporal and spatial scales, using only information about ...

The classical non-local means image denoising approach, the value of a pixel is determined based on the weighted average of other pixels, where the weights are determined based on a fixed isotropic ally weighted similarity function between the local neighbourhoods. It is demonstrate that noticeably improved perceptual quality can be achieved through the use of adaptive anisotropic ally weighted...

A novel multi-resolution cluster detection (MCD) method is proposed to identify irregularly shaped clusters in space. Multi-scale test statistic on a single cell is derived based on likelihood ratio statistic for Bernoulli sequence, Poisson sequence and Normal sequence. A neighborhood variability measure is defined to select the optimal test threshold. The MCD method is compared with single sca...

Hopkins statistic [@hopkins1954new] can be used to test for spatial randomness of data and detecting clusters in data. Although the method is nearly 70 years old, there persistent confusion regarding definition calculation statistic. We investigate its possible origin. Using most general statistic, we perform a small simulation verify distributional properties, provide visualization how calcula...

We propose a formal method to test stationarity for spatial point processes. The proposed test statistic is based on the integrated squared deviations of observed counts of events from their means estimated under stationarity. We show that the resulting test statistic converges in distribution to a functional of a two-dimensional Brownian motion. To conduct the test, we compare the calculated s...

As a useful tool for geographical cluster detection of events, the spatial scan statistic is widely applied in many fields and plays an increasingly important role. The classic version of the spatial scan statistic for the binary outcome is developed by Kulldorff, based on the Bernoulli or the Poisson probability model. In this paper, we apply the Hypergeometric probability model to construct t...

We introduce a formal testing procedure to assess the goodness-of-fit of a fitted inhomogeneous spatial Poisson process model. Our method is based on a discrepancy measure function Dc(t; θ̂) that is constructed by using residuals obtained from the fitted model. We derive the asymptotic distributional properties of Dc(t; θ̂) and then develop a test statistic based on these properties. Our test sta...

The test statistics Ih, Ic, and In are derived by decomposing the numerator of the Moran’s I test for high-value clustering, lowvalue clustering, and negative autocorrelation, respectively. Formulae to compute the means and variances of these test statistics are derived under a random permutation test scheme, and the p-values of the test statistics are computed by asymptotic normality. A set of...