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Geological records of past environmental change provide crucial insights into long-term climate variability, trends, non-stationarity, and nonlinear feedback mechanisms. However, reconstructing spatiotemporal fields from these records is statistically challenging due to their sparse, indirect, and noisy nature. Here, we present PaleoSTeHM, a scalable and modern framework for spatiotemporal hierarchical modeling of paleo-environmental data. This framework enables the implementation of flexible statistical models that rigorously quantify spatial and temporal variability from geological data while clearly distinguishing measurement and inferential uncertainty from process variability. We illustrate its application by reconstructing temporal and spatiotemporal paleo-sea-level changes across multiple locations. Using various modeling and analysis choices, PaleoSTeHM demonstrates the impact of different methods on inference results and computational efficiency. Our results highlight the critical role of model selection in addressing specific paleo-environmental questions, showcasing the PaleoSTeHM framework's potential to enhance the robustness and transparency of paleo-environmental reconstructions. 

Future sea-level rise projections are characterized by both quantifiable uncertainty and unquantifiable structural uncertainty. Thorough scientific assessment of sea-level rise projections requires analysis of both dimensions of uncertainty. Probabilistic sea-level rise projections evaluate the quantifiable dimension of uncertainty; comparison of alternative probabilistic methods provides an indication of structural uncertainty. Here we describe the Framework for Assessing Changes To Sea-level (FACTS), a modular platform for characterizing different probability distributions for the drivers of sea-level change and their consequences for global mean, regional, and extreme sea-level change. We demonstrate its application by generating seven alternative probability distributions under multiple emissions scenarios for both future global mean sea-level change and future relative and extreme sea-level change at New York City. These distributions, closely aligned with those presented in the Intergovernmental Panel on Climate Change Sixth Assessment Report, emphasize the role of the Antarctic and Greenland ice sheets as drivers of structural uncertainty in sea-level change projections. 

Abstract Luminous red novae (LRNe) are transients characterized by low luminosities and expansion velocities, and they are associated with mergers or common-envelope ejections in stellar binaries. Intermediate-luminosity red transients (ILRTs) are an observationally similar class with unknown origins, but they are generally believed to be either electron-capture supernovae in super-asymptotic giant branch stars or outbursts in dusty luminous blue variables (LBVs). In this paper, we present a systematic sample of eight LRNe and eight ILRTs detected as part of the Census of the Local Universe (CLU) experiment on the Zwicky Transient Facility (ZTF). The CLU experiment spectroscopically classifies ZTF transients associated with nearby (<150 Mpc) galaxies, achieving 80% completeness form_r< 20 mag. Using the ZTF-CLU sample, we derive the first systematic LRNe volumetric rate of ${7.8}_{-3.7}^{+6.5}\times {10}^{-5}$Mpc⁻³yr⁻¹in the luminosity range −16 ≤M_r≤ −11 mag. We find that, in this luminosity range, the LRN rate scales as $\mathit{dN}/\mathit{dL}\propto L^{-2.5\pm 0.3}$—significantly steeper than the previously derived scaling ofL^−1.4±0.3for lower-luminosity LRNe (M_V≥ −10 mag). The steeper power law for LRNe at high luminosities is consistent with the massive merger rates predicted by binary population synthesis models. We find that the rates of the brightest LRNe (M_r≤ −13 mag) are consistent with a significant fraction of them being progenitors of double compact objects that merge within a Hubble time. For ILRTs, we derive a volumetric rate of ${2.6}_{-1.4}^{+1.8}\times {10}^{-6}$Mpc⁻³yr⁻¹forM_r≤ −13.5 mag, which scales as $\mathit{dN}/\mathit{dL}\propto L^{-2.5\pm 0.5}$. This rate is ∼1%–5% of the local core-collapse supernova rate and is consistent with theoretical ECSN rate estimates.