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Variance estimation is an important aspect in statistical inference, especially in the dependent data situations. Resamplingmethods are ideal for solving this problem since these do not require restrictive distributional assumptions. In this paper, wedevelop a novel resampling method in the Jackknife family called the stationary jackknife. It can be used to estimatethe variance of a statistic in the cases where observations are from a general stationary sequence. Unlike the moving blockjackknife, the stationary jackknife computes the jackknife replication by deleting a variable length block and thelength has a truncated geometric distribution. Under appropriate assumptions, we can show the stationary jackknifevariance estimator is a consistent estimator for the case of the sample mean and, more generally, for a class of nonlinearstatistics. Further, the stationary jackknife is shown to provide reasonable variance estimation for a wider range ofexpected block lengths when compared with the moving block jackknife by simulation. 

Parametric computer-aided design (CAD) tools are the predominant way that engineers specify physical structures, from bicycle pedals to airplanes to printed circuit boards. The key characteristic of parametric CAD is that design intent is encoded not only via geometric primitives, but also by parameterized constraints between the elements. This relational specification can be viewed as the construction of a constraint program, allowing edits to coherently propagate to other parts of the design. Machine learning offers the intriguing possibility of accelerating the de- sign process via generative modeling of these structures, enabling new tools such as autocompletion, constraint inference, and conditional synthesis. In this work, we present such an approach to generative modeling of parametric CAD sketches, which constitute the basic computational building blocks of modern mechanical design. Our model, trained on real-world designs from the SketchGraphs dataset, autoregressively synthesizes sketches as sequences of primitives, with initial coordinates, and constraints that reference back to the sampled primitives. As samples from the model match the constraint graph representation used in standard CAD software, they may be directly imported, solved, and edited according to down- stream design tasks. In addition, we condition the model on various contexts, including partial sketches (primers) and images of hand-drawn sketches. Evaluation of the proposed approach demonstrates its ability to synthesize realistic CAD sketches and its potential to aid the mechanical design workflow. 

Fluctuations in temperature and precipitation are expected to increase with global climate change, with more frequent, more intense and longer-lasting extreme events, posing greater challenges for the security of global food production. Here we proposed a generic framework to assess the impact of climate-induced crop yield risk under both current and future scenarios by combining a stochastic model for synthetic climate generation with a well-validated statistical crop yield model. The synthetic climate patterns were generated using the extended Empirical Orthogonal Function method based on historically observed and projected climate conditions. We applied our framework to assess the corn and soybean yield risk in the U.S. Midwest for historical and future climate conditions. We found that: (1) in the U.S. Midwest, about 45% and 40% of the interannual variability in corn and soybean yield, respectively, can be explained by the climate; (2) the risk level is higher in the southwest and northwest regions of the U.S. Midwest corresponding to 25% yield reduction for both corn and soybean compared to other regions; (3) the severity for the 1988 and 2012 major droughts quantified by our method represent 21-year and 30-year events for corn, and 7-year and 12-year events for soybean, respectively; (4) the crop yield risk will increase under a future climate scenario (i.e., Representative Concentration Pathway 8.5 or RCP 8.5 at 2050) compared with the current climate condition, with averaged yield decreases and yield variability increases for both corn and soybean. The framework and the results of this study enable applications for risk management policies and practices for the agriculture sectors. 

Key challenges to regionalization of methane fluxes in the Amazon basin are the large seasonal variation in inundated areas and habitats, the wide variety of aquatic ecosystems throughout the Amazon basin, and the variability in methane fluxes in time and space. Based on available measurements of methane emission and areal extent, seven types of aquatic systems are considered: streams and rivers, lakes, seasonally flooded forests, seasonally flooded savannas and other interfluvial wetlands, herbaceous plants on riverine floodplains, peatlands, and hydroelectric reservoirs. We evaluate the adequacy of sampling and of field methods plus atmospheric measurements, as applied to the Amazon basin, summarize published fluxes and regional estimates using bottom-up and top-down approaches, and discuss current understanding of biogeochemical and physical processes in Amazon aquatic environments and their incorporation into mechanistic and statistical models. Recommendations for further study in the Amazon basin and elsewhere include application of new remote sensing techniques, increased sampling frequency and duration, experimental studies to improve understanding of biogeochemical and physical processes, and development of models appropriate for hydrological and ecological conditions. 

Abstract The complex interaction between the Indian Ocean dipole (IOD) and El Niño–Southern Oscillation (ENSO) is further investigated in this study, with a focus on the impacts of the IOD on ENSO in the subsequent year [ENSO(+1)]. The interaction between the IOD and the concurrent ENSO [ENSO(0)] can be summarized as follows: ENSO(0) can trigger and enhance the IOD, while the IOD can enhance ENSO(0) and accelerate its demise. Regarding the impacts of IOD(0) on the subsequent ENSO(+1), it is revealed that the IOD can lead to anomalous SST cooling patterns over the equatorial Pacific after the winter following the IOD, indicating the formation of a La Niña–like pattern in the subsequent year. While the SST cooling tendency associated with a positive IOD is attributable primarily to net heat flux (thermodynamic processes) from autumn to the ensuing spring, after the ensuing spring the dominant contribution comes from oceanic processes (dynamic processes) instead. From autumn to the ensuing spring, the downward shortwave flux response contributes the most to SST cooling over the central and eastern Pacific, due to the cloud–radiation–SST feedback. From the ensuing winter to the ensuing summer, changes in latent heat flux (LHF) are important for SST cooling, indicating that the release of LHF from the ocean into the atmosphere increases due to strong evaporation and leads to SST cooling through the wind–evaporation–SST feedback. The wind stress response and thermocline shoaling verify that local Bjerknes feedback is crucial for the initiation of La Niña in the later stage.