South African Statistical Journal

Seasonal catchment areas using an attribute based fuzzy lattice data structure

2025-03-30T13:00:19+00:00

Seasonality impacts various industries and sectors, influencing agricultural cycles, economic planning, and healthcare resource allocation. We propose a novel approach using an attribute based fuzzy lattice data structure to create overlapping catchment areas using the fundamentals of label propagation and graph clustering. This approach considers both the link structure and attribute similarities between nodes in a network, where the nodes are points of interest in a road network. Nodes may be close or far apart based on connectivity and shared attributes, such as common interests or in a geographical application considering topography features. In this study, we incorporate static and seasonal attributes for geographical nodes, allowing us to explore seasonal catchment areas and provide a more realistic view of accessibility throughout the year. This integrated approach offers a comprehensive framework for assessing spatial accessibility and understanding seasonal variations in regions to enhance planning for essential services.

On new tests for the Poisson distribution based on empirical weight functions

2025-03-30T13:00:20+00:00

We propose new goodness-of-fit tests for the Poisson distribution. The testing procedure entails fitting a weighted Poisson distribution, which has the Poisson as a special case, to observed data. Based on sample data, we calculate an empirical weight function which is compared to its theoretical counterpart under the Poisson assumption. Weighted L_p distances between these empirical and theoretical functions are proposed as test statistics and closed form expressions are derived for L₁, L₂ and L_∞ distances. A Monte Carlo study is included in which the newly proposed tests are shown to be powerful when compared to existing tests, especially in the case of overdispersed alternatives. We demonstrate the use of the tests with two practical examples.

A Bayesian mixture model accounting for individual heterogeneity in response to pathogenic infection

2025-03-30T13:00:20+00:00

The analysis of multivariate serological data derived from blood serum samples and tested for the presence of antibodies against multiple pathogens gained attention in recent years. Despite the common use of a so-called threshold approach to classify individuals as seronegative or -positive, limitations of such an approach have been reported in the literature, with the subjective choice of the threshold being the most important. Here, we consider a Bayesian mixture approach to model continuous IgG antibody concentrations directly while accounting for the presence of individual heterogeneity and implied association between antibody titer levels for two infections. We fitted the proposed model to Belgian bivariate serological data on the varicella-zoster virus (VZV) and parvovirus B19 (PVB19). Given the existing body of evidence with respect to possible reinfections with PVB19, we investigated whether models explicitly accounting for waning of humoral immunity improved model fit. Our results showed that although after a steep rise with age, the observed seroprevalence for PVB19 decreases between the ages of 20 and 40, the mean IgG antibody concentration remains constant with age among individuals in the seropositive component. This could provide evidence of a direct impact of reinfections with PVB19 on the observed IgG antibody levels, while individuals with loss of humoral immunity after natural infection imply an increase in susceptibility. For VZV, the mean IgG antibody levels slightly decrease with increasing age among seropositive individuals, indicating only very limited waning of humoral immunity as age-dependent seroprevalence estimates are monotonically increasing with increasing age. In general, based on our analyses, we showed that mixture models provide additional insights concerning the waning of humoral immunity as compared to more traditional frailty approaches, which focus on estimating the seroprevalence solely while the model is sufficiently flexible to capture observed dynamics in IgG antibody decay.