Except for about a half dozen papers, virtually all (co)authored by Griffith, the existing literature lacks much content about the interface between spatial optimization, a popular form of geographic analysis, and spatial autocorrelation, a fundamental property of georeferenced data. The popular
- Award ID(s):
- 1951344
- NSF-PAR ID:
- 10342691
- Date Published:
- Journal Name:
- Stats
- Volume:
- 4
- Issue:
- 4
- ISSN:
- 2571-905X
- Page Range / eLocation ID:
- 850 to 867
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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p ‐median location‐allocation problem highlights this situation: the empirical geographic distribution of demand virtually always exhibits positive spatial autocorrelation. This property of geospatial data offers additional overlooked information for solving such spatial optimization problems when it actually relates to their solutions. With a proof‐of‐concept outlook, this paper articulates connections between the well‐known Majority Theorem of the 1‐median minisum problem and local indices of spatial autocorrelation; the LISA statistics appear to be the more useful of these later statistics because they better embrace negative spatial autocorrelation. The relationship articulation outlined here results in the positing of a new proposition labeled the egalitarian theorem. -
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Abstract Regime shifts have large consequences for ecosystems and the services they provide. However, understanding the potential for, causes of, proximity to, and thresholds for regime shifts in nearly all settings is difficult. Generic statistical indicators of resilience have been proposed and studied in a wide range of ecosystems as a method to detect when regime shifts are becoming more likely without direct knowledge of underlying system dynamics or thresholds. These early warning statistics (EWS) have been studied separately but there have been few examples that directly compare temporal and spatial EWS in ecosystem‐scale empirical data. To test these methods, we collected high‐frequency time series and high‐resolution spatial data during a whole‐lake fertilization experiment while also monitoring an adjacent reference lake. We calculated two common EWS, standard deviation and autocorrelation, in both time series and spatial data to evaluate their performance prior to the resulting algal bloom. We also applied the quickest detection method to generate binary alarms of resilience change from temporal EWS. One temporal EWS, rolling window standard deviation, provided advanced warning in most variables prior to the bloom, showing trends and between‐lake patterns consistent with theory. In contrast, temporal autocorrelation and both measures of spatial EWS (spatial SD, Moran's
I ) provided little or no warning. By compiling time series data from this and past experiments with and without nutrient additions, we were able to evaluate temporal EWS performance for both constant and changing resilience conditions. True positive alarm rates were 2.5–8.3 times higher for rolling window standard deviation when a lake was being pushed towards a bloom than the rate of false positives when it was not. For rolling window autocorrelation, alarm rates were much lower and no variable had a higher true positive than false positive alarm rate. Our findings suggest temporal EWS provide advanced warning of algal blooms and that this approach could help managers prepare for and/or minimize negative bloom impacts. -
Spatial prediction is to predict the values of the targeted variable, such as PM2.5 values and temperature, at arbitrary locations based on the collected geospatial data. It greatly affects the key research topics in geoscience in terms of obtaining heterogeneous spatial information (e.g., soil conditions, precipitation rates, wheat yields) for geographic modeling and decision-making at local, regional, and global scales. In-situ data, collected by ground-level in-situ sensors, and remote sensing data, collected by satellite or aircraft, are two important data sources for this task. In-situ data are relatively accurate while sparse and unevenly distributed. Remote sensing data cover large spatial areas but are coarse with low spatiotemporal resolution and prone to interference. How to synergize the complementary strength of these two data types is still a grand challenge. Moreover, it is difficult to model the unknown spatial predictive mapping while handling the trade-off between spatial autocorrelation and heterogeneity. Third, representing spatial relations without substantial information loss is also a critical issue. To address these challenges, we propose a novel Heterogeneous Self-supervised Spatial Prediction (HSSP) framework that synergizes multi-source data by minimizing the inconsistency between in-situ and remote sensing observations. We propose a new deep geometric spatial interpolation model as the prediction backbone that automatically interpolates the values of the targeted variable at unknown locations based on existing observations by taking into account both distance and orientation information. Our proposed interpolator is proven to both be the general form of popular interpolation methods and preserve spatial information. The spatial prediction is enhanced by a novel error-compensation framework to capture the prediction inconsistency due to spatial heterogeneity. Extensive experiments have been conducted on real-world datasets and demonstrated our model’s superiority in performance over state-of-the-art models.more » « less
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ABSTRACT Fluctuations in Lyman-α (Ly α) forest transmission towards high-z quasars are partially sourced from spatial fluctuations in the ultraviolet background, the level of which are set by the mean free path of ionizing photons (λmfp). The autocorrelation function of Ly α forest flux characterizes the strength and scale of transmission fluctuations and, as we show, is thus sensitive to λmfp. Recent measurements at z ∼ 6 suggest a rapid evolution of λmfp at z > 5.0 which would leave a signature in the evolution of the autocorrelation function. For this forecast, we model mock Ly α forest data with properties similar to the XQR-30 extended data set at 5.4 ≤ z ≤ 6.0. At each z, we investigate 100 mock data sets and an ideal case where mock data matches model values of the autocorrelation function. For ideal data with λmfp = 9.0 cMpc at z = 6.0, we recover $\lambda _{\text{mfp}}=12^{+6}_{-3}$ cMpc. This precision is comparable to direct measurements of λmfp from the stacking of quasar spectra beyond the Lyman limit. Hypothetical high-resolution data leads to a $\sim 40~{{\ \rm per\ cent}}$ reduction in the error bars over all z. The distribution of mock values of the autocorrelation function in this work is highly non-Gaussian for high-z, which should caution work with other statistics of the high-z Ly α forest against making this assumption. We use a rigorous statistical method to pass an inference test, however future work on non-Gaussian methods will enable higher precision measurements.
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Context Engineering design skills are essential for engineering students to succeed in their careers. Engineering design is a skill that is in high demand in the current job market and should be prioritized in education. Purpose While design has been acknowledged as a cognitive skill in research, there exists limited literature addressing the cognitive foundations of design thinking. Hence, engineering educators must understand the engineering design process, as well as the different ways students approach design problem-solving and the potential reason behind these differences. To understand how people solve design problems, we need to consider how their minds work and the strategies they use. Spatial ability stands out as a cognitive factor that is crucial for designers and holds significance in well-established theories and models of intelligence. However, to date, research exploring the impact of spatial ability on design thinking and its influence on problem-scoping behaviors remains limited. This paper examines how engineering students’ spatial skills influence how they define the scope of open-ended design problems. The central research question that guides this paper is “How do design problem-scoping behaviors differ for engineering students based on their spatial scores?”. Methods The researchers used a mixed methods research approach to answer their research question, collecting qualitative and quantitative data in two phases. One hundred twenty-seven undergraduate engineering students completed four tests that measure spatial reasoning skills in the quantitative phase and 101 students returned to finish the three design tasks in the second phase. This paper will examine the performance of students with low spatial and high spatial skills on one of the completed design tasks. Outcomes From the study, it was clear that spatial skills have an impact on the design-scoping behaviors of the undergraduate engineering students. It was inferred that high spatial skill visualizers emphasized the technical details of the design problem whereas low spatial skill visualizers emphasized the context of the design problem during their problem-scoping behavior. A Mann-Whitney test revealed there was a statistically significant difference in detail- and context-focused segments between the high and low spatial visualizer groups. Conclusion This research study confirms that a relationship exists between spatial and design skills. The study also found that undergraduate engineering students with different levels of spatial skills had different approaches to scoping design problems.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/stats4040050
