Statistics — Page 2
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Global Co-Kriging
Global Co-Kriging is a multivariate geostatistical interpolation method that estimates an unsampled primary variable by exploiting its spatial cross-correlation with one or more secondary variables. Unlike local (moving-window) approaches,...
Global Getis-Ord Gi*
The Global Getis-Ord Gi* statistic measures the overall degree of spatial clustering of high or low values across an entire study region. It answers whether the study area, taken as a whole, exhibits significant concentration of high values...
Global Hot Spot Analysis
Global Hot Spot Analysis uses the Getis-Ord G statistic to determine whether high or low attribute values are spatially concentrated across an entire study area. It answers one question: is there overall clustering of high values (a hot spo...
Global Kriging
Global Kriging is the ordinary kriging interpolation procedure applied using all available sample points as the neighborhood — no spatial search window limits which data contribute to each prediction. It produces optimal linear unbiased pre...
Global Moran's I
Global Moran's I is the most widely used single-number summary of spatial autocorrelation across an entire study area. It compares the attribute value at each location with values at neighbouring locations using a spatial weights matrix, an...
Global Ordinary Kriging
Global Ordinary Kriging (GOK) is the canonical geostatistical interpolation method that estimates values at unsampled locations as a weighted linear combination of nearby observations. It fits a single variogram model to the entire dataset,...
Global Remote Sensing Classification
Global Remote Sensing Classification assigns every pixel across an entire image or worldwide dataset to a discrete land-cover or thematic class. Treating the scene uniformly — rather than adapting to local subregions — this wall-to-wall app...
Global Spatial Autocorrelation
Global Spatial Autocorrelation measures the degree to which similar values cluster together across an entire study area. Rather than identifying where clusters occur, it yields a single summary statistic — most commonly Moran's I — that qua...
Global Spatial Durbin Model
The Global Spatial Durbin Model extends the spatial lag model by including not only a spatially lagged dependent variable but also spatially lagged independent variables (WX). A single set of global coefficients applies uniformly across all...
Global Spatial Error Model
The Global Spatial Error Model (SEM) is a spatial regression technique that accounts for spatially autocorrelated error terms using a single, globally constant spatial parameter. It separates genuine predictor effects from spatial nuisance...
Global Spatial Panel Model
The Global Spatial Panel Model extends panel data regression by incorporating a global spatial weights matrix that links every location to every other location simultaneously. It jointly accounts for cross-sectional spatial dependence, time...
Global Universal Kriging
Global Universal Kriging is a geostatistical interpolation method that models a spatially varying trend (drift) as a deterministic function of coordinates and uses the entire dataset to fit both the trend coefficients and the residual vario...
Hot Spot Analysis
Hot Spot Analysis uses the Getis-Ord Gi* local spatial statistic to identify geographic locations where high or low attribute values cluster together to a degree that is statistically significant. Each feature is evaluated in relation to it...
Huff Model
Proposed by David Huff in 1964, the Huff Model is a probabilistic spatial interaction model that estimates the likelihood that consumers located in a given geographic zone will choose to shop at a particular retail outlet. It extends determ...
Inverse Distance Weighting
Inverse distance weighting is a simple, deterministic method for estimating values at unsampled locations by taking a weighted average of nearby measured points, where closer points carry more weight. Introduced by Donald Shepard in 1968, i...
Kriging
Kriging is a geostatistical method that predicts the value of a continuous variable at unmeasured locations from nearby measurements, using the spatial correlation structure captured by a variogram. Formalised by Georges Matheron in 1963, i...
LISA
LISA, introduced by Luc Anselin in 1995, is a local statistic that computes spatial autocorrelation separately for every observation rather than for the map as a whole. It pinpoints where high or low values cluster and where spatial outlier...
Local Geary's C
Local Geary's C is a local indicator of spatial association (LISA) that measures, for each location, how dissimilar its value is from its immediate neighbours. Unlike Local Moran's I, which detects clustering of similar values, Local Geary'...
Local Geographically Weighted Regression
Local Geographically Weighted Regression (GWR) estimates a separate regression model at each location in the study area, allowing every coefficient to vary spatially. By weighting nearby observations more heavily than distant ones, GWR reve...
Local Getis-Ord Gi*
The Local Getis-Ord Gi* statistic identifies statistically significant spatial clusters of high values (hot spots) and low values (cold spots) within a study area. Unlike global measures, it produces a z-score for every location, revealing...
Local Hot Spot Analysis
Local Hot Spot Analysis uses the Getis-Ord Gi* statistic to identify specific geographic locations where high or low values cluster together more than expected by chance. Unlike global measures that return a single summary for the whole stu...
Local Indicators of Spatial Association
LISA, introduced by Luc Anselin in 1995, decomposes a global spatial autocorrelation index into a location-specific statistic for every observation. It identifies where statistically significant spatial clusters and outliers occur on a map,...
Local Kernel Density Estimation
Local Kernel Density Estimation (Local KDE) is a non-parametric spatial method that estimates the density of point events at each location by applying a kernel function with a spatially adaptive bandwidth. Unlike global KDE, which uses a fi...
Local Kriging
Local Kriging is a spatially adaptive geostatistical interpolation method that restricts each prediction to a moving neighborhood of nearby observations, fitting a variogram model locally within that window. This allows spatial covariance s...