Recent advances in satellite technologies, statistical and mathematical models, and computational resources have paved the way for operational use of satellite data in monitoring and forecasting natural hazards. We present a review of the use of satellite data for Earth observation in the context of geohazards preventive monitoring and disaster evaluation and assessment. We describe the techniques exploited to extract ground displacement information from satellite radar sensor images and the applicability of such data to the study of natural hazards such as landslides, earthquakes, volcanic activity, and ground subsidence. In this context, statistical techniques, ranging from time series analysis to spatial statistics, as well as continuum or discrete physics-based models, adopting deterministic or stochastic approaches, are irreplaceable tools for modeling and simulating natural hazards scenarios from a mathematical perspective. In addition to this, the huge amount of data collected nowadays and the complexity of the models and methods needed for an effective analysis set new computational challenges. The synergy among statistical methods, mathematical models, and optimized software, enriched with the assimilation of satellite data, is essential for building predictive and timely monitoring models for risk analysis.

One of the most promising applications of satellite data is providing users in charge of land and emergency management with information and data to support decision making for geohazard mapping, monitoring and early warning. In this work, we consider ground displacement data obtained via interferometric processing of satellite radar imagery, and we provide a novel post-processing approach based on a Functional Data Analysis paradigm capable of detecting precursors in displacement time series. The proposed approach appropriately accounts for the spatial and temporal dependencies of the data and does not require prior assumptions on the deformation trend. As an illustrative case, we apply the developed method to the identification of precursors to a mud volcano eruption in the Santa Barbara village in Sicily, southern Italy, showing the advantages of using a Functional Data Analysis framework for anticipating the warning signal. Indeed, the proposed approach is able to detect precursors of the paroxysmal event in the time series of the locations close to the eruption vent and provides a warning signal months before a scalar approach would. The method presented can potentially be applied to a wide range of geological events, thus representing a valuable and far-reaching monitoring tool.

We analyze the proteomics data introducing a block $k$-mean alignment procedure. This technique is able to jointly align and cluster the data, accounting appropriately for the block structure of these data, that includes measurement repetitions for each patient. An analysis of area-under-peaks, following the alignment, separates patients who respond and those who do not respond to treatment.