This study evaluated ten drought indices focusing on their ability to monitor drought events in Marathwada, a semi-arid region of India. High-resolution gridded monthly total precipitation data for 75 years (1950–2024) from the European Centre for Medium-Range Weather Forecasts (ECMWF) were used to evaluate the drought indices. These indices were computed across six timescales: 1, 3, 4, 6, 9, and 12 months. A Generalized Autoregressive Conditional Heteroscedastic (GARCH) model was employed to detect temporal volatility in precipitation, followed by a second-order geospatial autocorrelation eigenfunction eigendecomposition using Global Moran’s Index statistics to geolocate both aggregated and non-aggregated precipitation locations. The performance of drought indices was assessed using non-parametric Spearman’s correlation to identify the strength, direction, and similarity of regional-specific drought events. The temporal lag interdependence between meteorological and agricultural droughts was assessed using a non-parametric Spearman’s cross correlation function (SCCF). The findings revealed that the GARCH model with a skewed Student’s t distribution effectively captured conditional temporal volatility and asymptotic behavior in the precipitation series. The model’s sensitivity enabled the incorporation of temporal fluctuations related to droughts and extreme meteorological events. The Bhalme and Mooley Drought Index (BMDI-6) and Z-Score Index (ZSI-6) were the most applicable indices for drought monitoring. Spearman’s cross-correlation analysis revealed that meteorological droughts influenced agricultural droughts with a time lag of up to 4 months.

Geographic variation (GV) in screening patterns for breast cancer exists among Zip Code Tabulation Areas (ZCTAs) in Florida, but most spatial analyses are based on frequentist point estimates which do not formally represent uncertainty. This study used a three-stage analytical approach to the breast cancer screening data at the zip code tract (ZCTA) level in Hillsborough County, Florida (n = 55 ZCTAs): first, a frequentist Poisson regression was applied with diagnostics for multicollinearity; second, global spatial autocorrelation (GSA) analysis was conducted using Moran’s I; and third, a Bayesian Poisson and a Bayesian negative binomial regression were performed, both estimated via the No-U-Turn Sampler in the brms/Stan framework. In ArcGIS Pro 3.6, spatial analyses were carried out. The dependent variable was the number of breast cancer screening exams conducted at the ZCTA level over the study period. Across all racial/ethnic subgroups, the observed number of screenings was correlated with the number of females in the household, while no independent correlation was found for median household income, insurance status or age by stratum variables after adjustment. There was no significant and strong spatial autocorrelation across the study area (Moran’s I = 0.003, z = 0.326, p = 0.745). The Poisson model did best among the Bayesian models with a Bayesian R² of 0.91, RMSE of 5.40, and MBE of 0.02. The results show the usefulness of Bayesian uncertainty quantification in small area public health surveillance and offer a framework for quantifying geographic variation in screening activity in a probabilistic manner. The results only compare screening examination (not population-standardized screening rates) and should be considered to reflect screening volume rather than screening participation.

Breast cancer screening patterns exhibit geographic variation across Zip Code Tabulation Areas (ZCTAs) in Florida, yet most spatial analyses rely on frequentist point estimation without formally characterizing uncertainty. This study applied a three-stage analytical framework to ZCTA-level breast cancer screening data in Hillsborough County, Florida (n = 55 ZCTAs): frequentist Poisson regression with stepwise multicollinearity diagnostics, global spatial autocorrelation analysis using Moran’s I with inverse-distance weighting, and Bayesian Poisson and Bayesian negative binomial regression with Jeffreys non-informative priors estimated via the No-U-Turn Sampler in R (brms/Stan). Spatial analysis was conducted in ArcGIS Pro. Racial and ethnic female population counts for White, Black or African American, and Hispanic or Latino groups were the strongest and most consistent predictors of screening counts. Median household income, insurance status, and age-stratified variables showed no independent association at the ZCTA level. Global Moran’s I was near zero and non-significant (I = 0.003, z = 0.326, p = 0.745). The Bayesian Poisson model showed superior fit compared with the Bayesian negative binomial model (Bayesian R² = 0.91, DIC = 367.2, RMSE = 5.40, MBE = 0.02). These findings associate screening concentration with the geographic distribution of demographic groups and demonstrate the value of a Bayesian uncertainty-oriented framework for small-area public health analysis.