Statistics
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Bayesian Co-Kriging
Bayesian Co-Kriging is a multivariate geostatistical method that uses auxiliary spatially correlated variables to improve predictions of a primary variable of interest. By placing Bayesian priors on cross-covariance parameters, it propagate...
Bayesian Geary's C
Bayesian Geary's C embeds the classical Geary contiguity ratio within a Bayesian hierarchical framework. Instead of a single point estimate and asymptotic p-value, it produces a posterior distribution over the statistic (or over spatially s...
Bayesian Geographically Weighted Regression
Bayesian Geographically Weighted Regression combines the spatially varying coefficient framework of GWR with Bayesian inference, placing Gaussian process priors on the locally varying regression coefficients. This yields full posterior dist...
Bayesian Hot Spot Analysis
Bayesian Hot Spot Analysis identifies spatial clusters of elevated risk or intensity by combining observed data with prior beliefs about spatial structure. It uses Bayesian smoothing — pooling information across neighboring areas — to stabi...
Bayesian Kernel Density Estimation
Bayesian Kernel Density Estimation (BKDE) is a nonparametric method for estimating the probability density function of a spatial or attribute variable by combining a kernel smoother with a Bayesian prior over the bandwidth parameter. The po...
Bayesian Kriging
Bayesian Kriging embeds classical geostatistical interpolation inside a full probabilistic framework. Instead of treating variogram parameters as fixed point estimates, it places prior distributions on them and updates these priors with obs...
Bayesian Local Indicators of Spatial Association
Bayesian Local Indicators of Spatial Association extend the classical LISA framework by embedding local spatial association statistics within a Bayesian hierarchical model. Rather than relying on asymptotic permutation-based significance te...
Bayesian Moran's I
Bayesian Moran's I embeds the classical Moran's I spatial autocorrelation test within a Bayesian probabilistic framework. Rather than producing a single p-value, it yields a posterior distribution over the spatial autocorrelation parameter,...
Bayesian Multiscale Geographically Weighted Regression
Bayesian Multiscale Geographically Weighted Regression (Bayesian MGWR) extends the MGWR framework by placing Bayesian priors on each spatially varying coefficient. Each predictor is allowed its own bandwidth — its own geographic scale of in...
Bayesian Ordinary Kriging
Bayesian Ordinary Kriging is a geostatistical interpolation method that combines classical ordinary kriging with a Bayesian framework to jointly estimate the spatial covariance parameters and produce predictions at unsampled locations. Unli...
Bayesian Spatial Autocorrelation
Bayesian Spatial Autocorrelation embeds spatial dependence directly into a Bayesian hierarchical model. A Conditional Autoregressive (CAR) prior encodes the expectation that neighboring areas are more similar than distant ones, and posterio...
Bayesian Spatial Durbin Model
The Bayesian Spatial Durbin Model (BSDM) estimates a spatial regression that simultaneously includes a spatially lagged outcome variable and spatially lagged covariates, using Bayesian inference with Markov Chain Monte Carlo sampling. It ca...
Bayesian Spatial Error Model
The Bayesian Spatial Error Model (Bayesian SEM) estimates a regression in which spatially correlated disturbances are explicitly modelled through a spatial weights matrix, while all parameters — regression coefficients, spatial error autoco...
Bayesian Spatial Lag Model
The Bayesian Spatial Lag Model (BSLM) extends the classical spatial autoregressive (SAR) regression by placing prior distributions over all parameters and recovering full posterior distributions via MCMC sampling. It explicitly accounts for...
Bayesian Spatial Panel Model
The Bayesian Spatial Panel Model estimates spatial interaction effects (spatial lag, spatial error, or Durbin) in panel data using Bayesian inference via Markov Chain Monte Carlo (MCMC). It combines the ability to control for unobserved uni...
Bayesian Spatial Regression
Bayesian Spatial Regression embeds a spatially structured random effect into a regression framework and estimates all parameters — including spatial range and variance — through posterior inference rather than point estimation. It handles s...
Bayesian Universal Kriging
Bayesian Universal Kriging (BUK) extends classical universal kriging by placing prior distributions on trend coefficients and spatial covariance parameters, then propagating full posterior uncertainty into predictions. It interpolates spati...
Co-kriging
Co-kriging is a geostatistical interpolation technique that predicts the spatial distribution of a primary variable by leveraging its spatial cross-correlation with one or more secondary (co-) variables. It extends ordinary kriging to multi...
Cokriging
Cokriging extends kriging to use one or more correlated secondary variables to improve prediction of a primary variable. When the variable of interest is sparsely sampled but a related, cheaper-to-measure variable is densely sampled, cokrig...
Conditional Geostatistical Simulation
Conditional Geostatistical Simulation — most commonly implemented as Sequential Gaussian Simulation (SGS) — generates multiple stochastic realizations of a spatial random field that are each consistent with observed sample data and with a f...
Geary's C
Geary's C is a global measure of spatial autocorrelation — whether nearby locations tend to have similar values — introduced by Roy Geary in 1954. Unlike Moran's I, which is built on the covariation of values around the mean, Geary's C is b...
Geary's C
Geary's C is a global spatial autocorrelation statistic that measures whether nearby areal units share similar attribute values. Unlike Moran's I, it focuses on squared differences between adjacent pairs rather than cross-products of deviat...
Geographically Weighted Regression
Geographically Weighted Regression is a local regression method, introduced by Fotheringham, Brunsdon and Charlton (2002), that allows the regression coefficients to vary across space. Instead of one global equation, it fits a separate set...
Getis-Ord Gi*
Getis-Ord Gi* is a local spatial statistic, introduced by Getis and Ord in 1992 and refined in 1995, that compares the value at each location and its neighbours against the global mean to identify statistically significant clusters of high...