Linganisha mbinu

	Besag-York-Mollie Model	Spatial Scan Statistic
Nyanja	Spatial Epidemiology	Spatial Epidemiology
Familia	Regression model	Process / pipeline
Mwaka wa asili	1991	1997
Mwanzilishi	Julian Besag, Jeremy York & Annie Mollie (BYM2 by Riebler, Sorbye, Simpson & Rue)	Martin Kulldorff (with Neville Nagarwalla)
Aina	Hierarchical Bayesian Poisson model with structured and unstructured spatial random effects	Likelihood-ratio scanning procedure for detecting and testing geographic disease clusters
Chanzo asilia	Besag, J., York, J., & Mollie, A. (1991). Bayesian image restoration, with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics, 43(1), 1-20.	Kulldorff, M. (1997). A spatial scan statistic. Communications in Statistics - Theory and Methods, 26(6), 1481-1496.
Majina mbadala	BYM Model, Convolution Prior Model, CAR Convolution Model, BYM2 Reparameterization	Kulldorff Scan Statistic, SaTScan Cluster Detection, Circular Scan Statistic, Spatial Likelihood-Ratio Scan
Zinazohusiana	4	4
Muhtasari	The Besag-York-Mollie (BYM) model is the workhorse hierarchical Bayesian model for small-area disease mapping. Proposed by Julian Besag, Jeremy York, and Annie Mollie (1991), it models area-level disease counts with a Poisson likelihood whose log relative risk is the sum of two random effects: a spatially structured component, given an intrinsic conditional autoregressive (ICAR) prior that borrows strength from neighboring areas, and an unstructured component capturing area-specific heterogeneity that is not spatially patterned. This convolution of structured and unstructured effects lets the model smooth noisy small-area rates toward local and global means while distinguishing genuine spatial trend from independent overdispersion. Because the original parameterization makes the two variance components hard to interpret and depends on the graph, Riebler, Sorbye, Simpson, and Rue (2016) introduced the scaled BYM2 reparameterization, which mixes a scaled spatial effect and an unstructured effect through a single interpretable mixing parameter and a total-variance parameter, improving prior specification and identifiability.	The spatial scan statistic is a likelihood-ratio method for detecting localized clusters of disease without pre-specifying where they are. Introduced by Martin Kulldorff and Neville Nagarwalla (1995) and generalized by Kulldorff (1997), it slides a circular window of varying size and position across the study region, and for each candidate window compares the observed-to-expected case ratio inside the window against outside it using a likelihood ratio under a Poisson or Bernoulli model. The window that maximizes the likelihood ratio is the most likely cluster, and its statistical significance is obtained by Monte Carlo simulation under the null of no clustering, which correctly accounts for the enormous multiplicity of windows examined. Implemented in the widely used SaTScan software, the method has become the standard tool for screening surveillance data for spatial and space-time disease clusters.