climate data analysts

Abstract: Machine-learning rainfall forecasts are often evaluated by shuffling station records into random training and test sets. For rainfall, this lets a model see what happened at neighbouring stations on the very day it is asked to forecast, and it hides the fact that a seasonal lookup table already explains most of the variance. We quantify both effects on 618,650 station-days from 35 Bangladesh Meteorological Department stations (1948-2014). We compare random, temporal (train <=1999, test 2005-2014) and spatio-temporal (unseen stations and unseen years) evaluation, calendar-only versus antecedent-rainfall features, and six learners against climatology, persistence and SARIMA. Three findings stand out. First, a station-month climatology alone classifies high-rainfall months with 88.4% accuracy (AUC 0.950), and no learner improved on it by more than 0.8 points under temporal evaluation. Second, a calendar-only random forest reached a next-day wet-day AUC of 0.889 under a random split, higher than any model with real predictors under temporal evaluation, yet fell to 0.835, below climatology (0.859), on future years. Third, models with lagged rainfall add genuine but modest skill for next-day forecasts: a Brier skill score of 0.074 (95% CI 0.064-0.088) over climatology, rising to 0.091 when station and year inputs are removed and to 0.131 when other stations' same-day observations are added. A GRU sequence model matches but does not exceed gradient boosting, and skill disappears beyond a two-day lead. For monthly totals, no learner beat climatology significantly. We release a leakage-aware protocol and code so that future station-based studies report skill against climatology on held-out years.

Abstract: Diffusion models typically learn the generative dynamics of a single target distribution or a family of distributions indexed by conditioning variables fixed during training. This limits their ability to adapt to a previously unseen distribution from only a small set of examples. We introduce an in-context solution operator learning framework for diffusion models, in which each target distribution is treated as a task drawn from a meta-distribution and is specified at inference time by an empirical context set. Our method learns an in-context score operator that maps the context samples, a noisy query point, and the diffusion time to the task-dependent score, enabling reverse-diffusion sampling on unseen tasks without retraining or parameter updates. A key observation is that the task-dependent score admits a Gaussian-kernel conditional-mean representation. Its empirical Nadaraya--Watson approximation can be represented exactly by a model in our constructed transformer class, providing a principled foundation for the proposed query-dependent attention architecture. The operator is trained through amortized denoising score matching across task distributions. We establish generalization-error bounds that quantify the effects of the context size, the numbers of training tasks and within-task samples, model complexity, and intrinsic and ambient dimensions. Numerically, we evaluate the method on a range of scientific and visual datasets, including Navier-Stokes, ERA5 climate data, QuickDraw sketches, and Food-101. The results show that the proposed method performs well on relatively simple task families, while its performance degrades as task complexity increases, thereby illustrating both the promise and the limitations of in-context learning for diffusion models.

Abstract: Aerosol particles play a critical role in air quality, human health, and climate processes, making their accurate characterization essential. One common way to represent aerosol populations is through particle number size distributions (PNSDs), which describe the concentration of particles across different mobility diameters. However, these distributions are often highly skewed, heavy-tailed, and multi-modal, posing significant challenges for conventional fitting approaches. In this study, we propose a robust parametric framework (AeroMiG) for modeling PNSDs using Inverse-Gamma mixture distributions. The method represents observed size distributions as a superposition of multiple Inverse-Gamma components, enabling flexible modeling of asymmetric and heavy-tailed structures that are not well captured by widely-used Log-Gaussian based approaches. The performance of the proposed method is evaluated using real-world data from three measurement stations. Results are assessed using multiple criteria, including predictive accuracies, computational efficiency, and a composite score summarizing overall model quality. Comparative analysis against a widely used Aerosol Multi-mode Log-Gaussian (AeroMG) demonstrates that the AeroMiG framework consistently achieves improved fitting accuracy, lower error, and faster computation. The proposed approach provides a reliable and computationally efficient solution for modeling complex aerosol size distributions, with potential applications in real-time air quality monitoring and data-driven environmental analysis.

Abstract: Many scientific graphs attach several variables to each node, so a single scalar edge weight cannot describe direction-dependent interactions. We model each edge by a symmetric positive-definite (SPD) matrix and infer a posterior over matrix-valued graph geometries, which we call the Bayesian matrix-valued graph (BMVG). We ask how these interactions reconfigure across contexts: how large the change is and which multivariate directions strengthen or weaken. The geodesic distance induced by the affine-invariant Riemannian metric (AIRM) quantifies deformation magnitude and generalized eigenvalues resolve its signed directions.Against fused graphical lasso, Bayesian multiple-GGM, and common principal components, BMVG is competitive on global precision recovery while retaining identifiable matrix-valued edge structure and accurately recovering edge-level deformation directions. In controlled known-truth experiments, it resolves structural change with increasing sample size, including orientation changes that leave ordinary eigenvalues unchanged. In one year of Bay Area weather data, the geometry of 12-hour change reconfigures spatial coupling about as much as whole seasons differ. In TCGA-BRCA, estrogen-receptor (ER)-associated reconfiguration concentrates on specific gene-module pairs and persists under graph-scaffold sparsification and removal of subgroup mean differences. These results establish posterior matrix-valued edge geometry as a unified framework for quantifying and interpreting context-dependent multivariate reconfiguration.