Environmental statistics is one of the named theme areas of the 66th ISI World Statistics Congress, and its methodological challenges are intensifying. Climate change, biodiversity loss, pollution monitoring, and resource management generate heterogeneous, spatially structured, and often geometrically constrained data that standard methods cannot adequately handle. This session responds through two complementary, mutually reinforcing frameworks. Directional statistics addresses data on manifolds — wind direction, current bearing, animal orientation — yet remains largely absent from mainstream training and software. Advanced mixture models capture the heterogeneous, multimodal, and compositional structure of environmental datasets while preserving interpretability and computational tractability.
The Lusaka setting gives the session particular resonance. Africa faces some of the world’s most pressing environmental data challenges — climate variability, desertification, conservation monitoring, water resources — yet a capacity gap remains in applying rigorous methodology, especially within emerging institutions. By showcasing cutting-edge methods with explicit environmental application, the session supports the congress’s goals of equitable capacity-building. It also aligns with the AI-era theme, offering principled, interpretable alternatives to black-box approaches that integrate naturally with modern computation.

The panel reflects deliberate attention to the ISI’s diversity requirements across geography, gender, and seniority. It is organised from South Africa by Priyanka Nagar (Stellenbosch University) and Andriette Bekker (Emeritus Professor, University of Pretoria), with discussion led by two discussants spanning both frameworks: Antonio Punzo (University of Catania, Italy) and Andriette Bekker. The five speakers are based across Europe, Asia, and North America — extending the panel’s reach to four continents — with national backgrounds spanning Italy, Japan, Tunisia, and India. Women form the large majority of contributors, and the panel combines senior, mid-career, and early-career researchers.

The contributions span both pillars (directional statistics and model-based clustering) and each addresses a concrete environmental data problem. Cristina Tortora adapts skew normal-scale mixtures to cluster data missing at random — pervasive in environmental records truncated by detection limits, sensor failures, or sampling constraints — retaining partially observed cases via the new MixtureMissing R package. Shogo Kato introduces a projected-normal copula for hypertoroidal data with, unlike earlier projection models, interpretable parameters and latent-variable MCMC, demonstrated on Gulf of Mexico wind and wave directions. Houyem Demni develops robust M-estimation for circular environmental variables such as wind direction, ocean currents, and animal-movement trajectories, proposing a circular S-estimator with established influence-function and breakdown properties and a robust circular-regression extension under contamination. Shuchismita Sarkar models latent edge-level structure in dynamic multilayer environmental networks, grouping interactions among locations into latent classes by temporal and cross-layer behaviour. Sanjeena Dang proposes a logistic matrix-normal multinomial mixture for longitudinal compositional microbiome data — soil, marine, and host-associated — jointly modelling composition and temporal dependence with scalable variational-Gaussian estimation. Collectively the talks advance directional inference, robust estimation, copula modelling, network clustering, and compositional mixtures, each tackling an irregularity — angular geometry, outliers, missingness, network heterogeneity, over-dispersion — at the core of environmental practice.