Spatial statistics (Mathematics)

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Using Spatial Statistics In GIS

Geostatistical Analyst has several thousands of users and they have very different backgrounds and interests. Unfortunately, many researchers use the software only to make maps. Many statisticians do not understand or appreciate the full utility of GIS for spatial data analysis. Other researchers are not educated in spatial statistics, so they are unaware of techniques for modeling uncertainty, even though they realize that measuring and modeling without errors is impossible. At the same time, they readily use automatic “geoprocessing” tools that arithmetically add or average raster data values in the cells without taking into account the impact of error propagation on the results. After several such geoprocessing steps, the resulting data structure can be completely random and, consequently, decisions made from these results may be wrong. Still others use the software for analyses for which it was not designed. This problem often arises when users implement Geostatistical Analyst with aggregated data that are associated with spatially discrete units. For example, we have watched users discuss which interpolator, inverse squared distance weighting or splines, is better for mapping of proportions of females in burial populations. What is the best prediction of the proportion of females outside cemeteries? One would hope it is zero. There are other methods in spatial statistics that are more suitable for this type of data. For example, a marked point pattern analysis that incorporates an attribute value recorded at each location could be used. The mark would be the occurrence (or not) of a female burial at each location, and a marked point pattern model could then be used to estimate and map the intensity of females in burial populations, assuming that data point locations are given by nature and not selected by the user. Hopefully, all of these problems can be solved by education. Case studies can help to show users how GIS can and should be used for more sophisticated statistical analysis and modeling. 3. IMPROVED SPATIAL DATA

<p>The Implication of Spatial Statistics in Human Mesenchymal Stem Cell Response to Nanotubular Architectures</p>

In this work, we aimed at bridging the gap in previous literature by introducing a series of morphological and spatial analyses for the characterization of nanotubular architectures, culminating in the descriptive analysis of nanotubular surfaces towards a cohesive investigation of cell-nanotube interactions. To this end, we investigated three nanotubular arrays with variable nanotube diameters and a two-tiered honeycomb structure. Successively, we carried out morphological and spatial analysis (e.g., Voronoi entropy) to quantify the tubular geometry, arrangement as well as degree of order for these architectures. Our experimental data was validated by compu- tational simulations to provide greater insight into the role of morphological parameters and spatial statistics. Subsequently, we evaluated the effects of the four surfaces on hMSC bioac- tivity (i.e., proliferative and morphological analyses) and osteogenic induction (e.g, commitment to osteogenic differen- tiation and bone mineral quality). Results from our study (i) highlight the importance of including additional morphological analyses and spatial statistics in the characterization of nano- tubular surfaces for the purpose of enhancing the validity of cross-study comparisons, (ii) provide a comprehensive corre- lation between a multifactorial array of these parameters and hMSC activity extending from adhesion to bone mineral deposition, and lastly (iii) report the synergistic effects elicited by the HC architecture.

Stochastic simulation and spatial statistics of large datasets using parallel computing

Lattice models are a way of representing spatial locations in a grid where each cell is in a certain state and evolves according to transition rules and rates dependent on a surrounding neighbourhood. These models are capable of describing many phenom- ena such as the simulation and growth of a forest fire front. These spatial simulation models as well as spatial descriptive statistics such as Ripley’s K-function have wide applicability in spatial statistics but in general do not scale well for large datasets. Parallel computing (high performance computing) is one solution that can provide limited scalability to these applications. This is done using the message passing in- terface (MPI) framework implemented in R through the Rmpi package. Other useful techniques in spatial statistics such as point pattern reconstruction and Markov Chain Monte Carlo (MCMC) methods are discussed from a parallel computing perspective as well. In particular, an improved point pattern reconstruction is given and imple- mented in parallel. Single chain MCMC methods are also examined and improved upon to give faster convergence using parallel computing. Optimizations, and compli- cations that arise from parallelizing existing spatial statistics algorithms are discussed and methods are implemented in an accompanying R package, parspatstat.

MULTICLASS PATTERN RECOGNITION OF THE GLEASON SCORE OF PROSTATIC CARCINOMAS USING METHODS OF SPATIAL STATISTICS

The Gleason score of a prostatic carcinoma is generally considered as one of the most important prognostic parameters of this tumour type. In the present study, it was attempted to study the relation between the Gleason score and objective data of spatial statistics, and to predict this score from such data. For this purpose, 25 T1 incidental prostatic carcinomas, 50 pT2N0, and 28 pT3N0 prostatic adenocarcinomas were characterized by a histological texture analysis based on principles of spatial statistics. On sectional images, progression from low grade to high grade prostatic cancer in terms of the Gleason score is correlated with complex changes of the epithelial cells and their lumina with respect to their area, boundary length and Euler number per unit area. The central finding was a highly significant negative correlation between the Gleason score and the Euler number of the epithelial cell phase per unit area. The Gleason score of all individual cases was predicted from the spatial statistical variables by multivariate linear regression. This approach means to perform a multiclass pattern recognition, as opposed to the usual problem of binary pattern recognition. A prediction was considered as acceptable when its deviation from the human classification was no more than 1 point. This was achieved in 79 of these 103 cases when only the Euler number density was used as predictor variable. The accuracy could be risen slightly to 84 of the 103 cases, when 7 input variables were used for prediction of the Gleason score, which means an accuracy of 81.5%.

Contributions to Spatial Statistics and Big Data Analytics.

weather-related processes has similar importance as temporal prediction because, as men- tioned by Cressie (1993), “spatial prediction is just as important as temporal prediction, because people living those cities and rural districts without monitoring stations have the same right to know how little or how much their water or their air is polluted.” Most of the spatial prediction of weather-related processes are based on data collected by high- performance sensors at meteorological stations or images captured by high-resolution cameras in satellites. Recently, with the advancement of mobile sensor-related technology, geo-tagged weather information is being collected by micro-sensors installed in mobile devices and gathered by mobile weather applications like AccuWeather, WeatherSignal etc. These datasets are often referred as ‘crowdsourced’ weather data as the information is coming from the mobile application users. Standard methodologies in geostatistics or spatial statistics is not directly applicable to these mobile sensor-generated data as quality of the observations are often hampered in crowdsourced datatsets due to several factors: the low-quality of the sensors, indoor-outdoor user activity, influence of exter- nal and internal processes etc. to name a few. Developing data-driven robust as well as scalable methodologies to analyze noisy spatial data like crowdsourced weather data is broad focus of this dissertation.

A spatial statistics examination of changes in violent crime patterns following a housing redevelopment project

While this study provides hints at strong effects underlying the spatial distribution of violent crime in Durham and how projects like HOPE VI may alter that distribution, for the most part they remain hints. Similar work with spatial statistics to provide stronger, more robust understanding of these distributions would require both additional data sources, quantifying the many factors which might contribute to the changes in spatial distribution, as well as multivariate statistical techniques in addition to the univariate techniques used in this study. As discussed earlier, the most meaningful if potentially difficult additional factor which could be added to this study would be a spatially explicit representation of the vulnerable population. This conceivably could be developed as an activity model incorporating residential, employment, and retail data, as well as traffic counts and transportation models. Alternately, a spatial interpolation model could be built from empirically collected activity counts at key areas of the city. Even here, however, spatial interpolation becomes difficult, because activity counts do not vary smoothly along Euclidean distances, but follow rigid features of the urban landscape.

White matter connectivity in children with autism spectrum disorders: a tract-based spatial statistics study

Background: Autism spectrum disorders (ASD) are associated with widespread alterations in white matter (WM) integrity. However, while a growing body of studies is shedding light on microstructural WM alterations in high-functioning adolescents and adults with ASD, literature is still lacking in information about whole brain structural connectivity in children and low-functioning patients with ASD. This research aims to investigate WM connectivity in ASD children with and without mental retardation compared to typically developing controls (TD). Methods: Diffusion tensor imaging (DTI) was performed in 22 young children with ASD (mean age: 5.54 years) and 10 controls (mean age: 5.25 years). Data were analysed both using the tract-based spatial statistics (TBSS) and the tractography. Correlations were investigated between the WM microstructure in the identified altered regions and the productive language level.

Utilizing spatial statistics to identify cancer hot spots: a surveillance strategy to inform community-engaged outreach efforts

Given the vast toolset spatial epidemiologists have at their disposal, including a variety of global and local clustering statistics as well as descriptive spatial statistics, it is im- portant to establish appropriate evidence-based method- ologies. These analyses found that local spatial statistics tended to generally agree on where clusters occurred, with regions within Alachua County, Florida, USA consistently showing clustering, regardless of minority status. Figures 3 and A1 (see Additional file 1) show smaller, more lo- calized cancer clusters among minority members within rural areas of the county than those who were non- minority members, with “hot spots” located in the west and southwest rural areas. Such findings may be used not only to direct ongoing and future outreach efforts, but may have policy implications within the area in terms of service assessment and resource allocation. Further, these findings are consistent with previous oncological litera- ture, suggesting minority populations, particularly in rural areas throughout the US have disproportionately high cancer morbidity and mortality. This may potentially be a result of increased barriers to obtaining preventa- tive screenings which can catch lesions before cancer progression [20]. The results of these analyses therefore suggest that if patterns are present on the landscape, such local clustering techniques may have the appropri- ate resolution to consistently identify them, regardless of test statistic used.

Altered white matter integrity in individuals with cognitive vulnerability to depression: a tract-based spatial statistics study

mricro/mricron/dcm2nii.html) was used to convert the raw DICOM files from the proprietary scanner format to the nifti format, ‘‘.image’’. The diffusion-weighted images were analysed using the Functional Magnetic Resonance Imaging of the Brain Library (FSL, Oxford, United Kingdom). Briefly, the FSL eddy-correct tool was used to register all diffuse images in the B0 image space. The FSL bet2 was then used to skull- strip the brain to ensure that only tensors inside the brain were calculated, rather than those in the surrounding air, using a threshold of 0.25. Finally, a FSL DTIFIT tool was applied to calculate the diffusion tensor model at each pixel and obtain a FA image map. After data processing, tract-based spatial statistics (TBSS) 42 were used to explore

Tract Based Spatial Statistics in Preterm Born Neonates Predicts Cognitive and Motor Outcomes at 18 Months

RESULTS: Tract-based spatial statistics analysis applied to early-acquired scans (postmenstrual age of 30 –33 weeks) indicated a limited signiﬁcant positive association between motor skills and axial diffusivity and radial diffusivity values in the corpus callosum, internal and external/extreme capsules, and midbrain (P ⬍ .05, corrected). In contrast, for term scans (postmenstrual age of 37– 41 weeks), tract-based spatial statistics analysis showed a signiﬁcant relationship between both motor and cognitive scores with fractional anisotropy in the corpus callosum and corticospinal tracts (P ⬍ .05, corrected). Tract-based spatial statistics in a limited subset of neonates (n ⫽ 22) scanned at ⬍ 30 weeks did not signiﬁcantly predict neurodevelopmental outcomes.

Spatial Statistics and Age Structure of Leaf Cutting Ant Nests

DOI: 10.4236/ojs.2019.92015 211 Open Journal of Statistics to the growing demand for younger trees, thanks to intense selection of clones [21]. This demand results in the systematic rotation of trees in Eucalyptus areas, a reason why probably ant nests are aggregated in borders, especially between native forest and Eucalyptus plantations or Cerrado and Eucalyptus plantations. With the rotation of trees, the number of leaves available to supply ant nests de- creases drastically and incipient nests can be rapidly eliminated, increasing the risk that ant populations will fail to persist. However, old nests easily persist to the next Eucalyptus planting, using other resources. A variety of resources can be obtained by workers living in old nests because they are capable of foraging for much longer distances than workers in incipient nests [22].

Modelling malaria treatment practices in Bangladesh using spatial statistics

Because malaria treatment-seeking practices differ around the world [5-21], no universal strategy can be developed to tackle the issue of malaria incidence and treatment. Efforts to tailor malaria control programmes to local needs, requires an understanding of the factors that influence individual treatment-seeking practices. In this paper, spatial pattern analysis techniques and spatial regression are used to illustrate where national control programme services are well-utilized and where they are under-utilized, to identify the factors contributing to alternative treatment-seeking preferences, and to assess how the predictive strength of those factors change across the study area. Understanding where each factor is a strong predictor of treatment-seeking preferences can inform the design of targeted interventions aimed at increasing control programme utilization. Given the results of the spatial analysis presented, a variety of pos- sible intervention strategies are suggested.

Neonatal Tract Based Spatial Statistics Findings and Outcome in Preterm Infants

A second set of registrations was then performed to register every indi- vidual FA map to the mean FA map. The aligned images were then used to create another mean FA map and a mean FA skeleton, which represented the centers of all tracts common to the group. This FA skeleton was thresholded at FA ⱖ 0.15 to exclude peripheral tracts with high intersubject variability and/orpartialvolumeeffectswithgraymatter.Eachsubjects’alignedFA,AD, and RD data were projected onto this mean FA skeleton. Voxelwise cross- subject statistics was performed to assess the relationship between FA, AD, and RD and performance scores of the BSITD-III, corrected for gestational age and postmenstrual age at the time of the scanning. The results were cor- rected for multiple comparisons by controlling the family-wise error rate following TFCE. 23

Tract Based Spatial Statistics of Diffusion Tensor Imaging in Adults with Dyslexia

aged brain developed by the Montreal Neurological Institute). Sec- ond, the transformed FA images are averaged to create a mean FA image. Third, the mean FA is fed into the tract skeleton generation, which aims to represent all of the tracts that are “common” to all of the subjects. The skeleton will represent each such tract as a single line (or surface) running down the center of the tract. To achieve skeleton- ization, the local surface perpendicular direction is estimated (at all of the voxels in the image), and a nonmaximum suppression in this direction is performed. In other words, a search is made along all of the voxels in the local ‘‘tract perpendicular direction,” and the voxel with the highest FA is identified as the center of the tract. The esti- mated tract perpendicular direction is regularized to improve estima- tion robustness. Fourth, the center of each tract is found by compar- ing the FA value with the 2 closest neighbors on each side, in the direction of the tract perpendicular. If the FA value is greater than the neighboring values, then the voxel is marked as lying on the skeleton. Each subject’s aligned FA data were then projected onto this skel- eton (Fig 1), and the resulting data were fed into voxelwise cross- subject statistics. A randomization procedure (FSL’s randomize, Monte Carlo permutation test) was used to perform the group anal- ysis statistics. TBSS group maps were generated for the nonparamet- Table 1: Means, SDs, and values of t comparing means on psychological measures for control subjects and adults with dyslexia

Fractional imputation method of handling missing data and spatial statistics

Inference in the presence of missing data is a widely encountered and difficult problem in statistics. Imputation is often used to facilitate parameter estimation, which allows one to use the complete sample estimators on the imputed data set. In Chapter 2, We develop a parametric fractional imputation (PFI) method proposed by Kim (2011), which simplifies the computation associated with the EM algorithm for maximum likelihood estimation with missing data. We first consider the problem of parameter estimation for linear mixed models with non-ignorable missing values, which assumes that missingness depends on the missing values only through the random effects, leading to shared parameter models (Follmann and Wu,1995). In the M- step, the restricted or adjusted profiled maximum likelihood method is used to reduce the bias of maximum likelihood estimation of the variance components. Results from a limited simulation study are presented to compare the proposed method with the existing methods, which demonstrates that imputation can significantly reduce the non-response bias and the idea of adjusted profiled maximum likelihood works nicely in PFI for the bias correction in estimating the variance components. Variance estimation is also discussed. We next extend PFI to generalized linear mixed model and the flexibility of this method is illustrated by analyzing the infamous salamander mating data (McCullagh and Nelder, 1989).

A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics

Table 2: True values of σ12 and approximates of the NBias, NVar and NMSE for MBB and SPB estimators σ ˆ12 based on exponential covariogram.. Table 3: True values of σ12 and approximates [r]

A diffusion-weighted imaging tract-based spatial statistics study of autism spectrum disorder in preschool-aged children

In the current study, we sought to characterize WM diffusion properties associated with ASD in a sample of male and female preschool-aged children. We utilize DWI acquired during natural nocturnal sleep [47] to in- vestigate measures of FA, MD, RD, and AD across whole brain WM using a voxel-wise tract-based spatial statis- tics (TBSS) approach [54]. We hypothesize that individ- uals with ASD will have significant differences in WM diffusion properties in tracts previously indicated in the condition, including the corpus callosum and superior longitudinal fasciculus. To our knowledge, our study represents the largest diffusion imaging study in terms of inclusion of preschool-aged females with ASD. Based on prior DWI findings from our group reporting signifi- cant sex differences in TD [55] and diagnosis-by-sex interaction effects in ASD [52], we anticipate both a sig- nificant main effect of sex and diagnosis-by-sex interac- tions in diffusion measures.

White Matter Alteration in Idiopathic Normal Pressure Hydrocephalus: Tract Based Spatial Statistics Study

other one to identify the most representative one, and this image was used as the target image. This target image was then affine-aligned into MNI 152 standard space, and every image was transformed into 1 ⫻ 1 ⫻ 1 mm MNI 152 space by combining the nonlinear transform to the target FA image with the affine transform from the target native space to MNI 152 space. The mean FA image was created and thinned to create the mean FA skeleton, which represented the centers of all tracts common to the groups. This skeleton was thresholded at FA ⬎ 0.25. Each subject’s aligned FA map was then projected onto the skel- eton by assigning each point on the skeleton the maximum FA in a plane perpendicular to the local skeleton structure. The resulting skel- etons were fed into voxelwise statistics. The number of permutations was set to 5000. By using the TBSS results for the FA maps, we also analyzed maps of axial eigenvalues, radial eigenvalues, and ADC val- ues by TBSS analysis.