A spatiotemporal weighted regression model (STWR v1.0) for analyzing local nonstationarity in space and time
TL;DR: This research validates the ability of STWR to take full advantage of all the value variation of past observed points and hopes it can bring fresh ideas and new capabilities for analyzing and interpreting local spatiotemporal nonstationarity in many disciplines.
Abstract: . Local spatiotemporal non-stationarity occurs in various natural and socioeconomic processes. Many studies have attempted to introduce time as a new dimension into the geographically weighted regression model (GWR), but the actual results are sometimes not satisfied or even worse than the original GWR model. The core issue here is a mechanism for weighting effects of both temporal variation and spatial variation. In many geographical and temporal weighted regression models (GTWR), the concept of time distance has been inappropriately treated as time interval. Consequently, the combined effect of temporal and spatial variation is often inaccurate in the resulting spatiotemporal kernel function. This limitation restricts the configuration and performance of spatiotemporal weights in many existing GTWR models. To address this issue, we propose a new spatiotemporal weighted regression (STWR) model and the calibration method for it. A highlight of STWR is a new temporal kernel function, in which the method for temporal weighting is based on the degree of impact from each observed point to a regression point. The degree of impact, in turn, is based on the rate of value variation of the nearby observed point during the time interval. The updated spatiotemporal kernel function is based on a weighted combination of the temporal kernel with a commonly used spatial kernel (Gaussian or bi-square) by specifying a linear function of spatial bandwidth versus time. Three simulated datasets of spatiotemporal processes were used to test the performance of GWR, GTWR and STWR. Results show that STWR significantly improves the quality of fit and accuracy. Similar results were obtained by using real-world data for the precipitation hydrogen isotopes (δ2H) in Northeastern United States. The Leave-one-out cross-validation (LOOCV) test demonstrates that, comparing with GWR, the total prediction error of STWR is reduced by using recent observed points. Prediction surfaces of models in this case study show that STWR is more localized than GWR. Our research validates the ability of STWR to take full advantage of all the value variation of past observed points. We hope STWR can bring fresh ideas and new capabilities for analyzing and interpreting local spatiotemporal non-stationarity in many disciplines.
Citations
More filters
TL;DR: In this paper, the authors use mobile phone, census, and volunteered geographical data to measure geographic variations in the relationship between origin-destination flows and local urban accessibility in Barcelona.
Abstract: As cities expand, human mobility has become a central focus of urban planning and policy making to make cities more inclusive and sustainable. Initiatives such as the "15-minutes city" have been put in place to shift the attention from monocentric city configurations to polycentric structures, increasing the availability and diversity of local urban amenities. Ultimately they expect to increase local walkability and increase mobility within residential areas. While we know how urban amenities influence human mobility at the city level, little is known about spatial variations in this relationship. Here, we use mobile phone, census, and volunteered geographical data to measure geographic variations in the relationship between origin-destination flows and local urban accessibility in Barcelona. Using a Negative Binomial Geographically Weighted Regression model, we show that, globally, people tend to visit neighborhoods with better access to education and retail. Locally, these and other features change in sign and magnitude through the different neighborhoods of the city in ways that are not explained by administrative boundaries, and that provide deeper insights regarding urban characteristics such as rental prices. In conclusion, our work suggests that the qualities of a 15-minutes city can be measured at scale, delivering actionable insights on the polycentric structure of cities, and how people use and access this structure.
21 citations
TL;DR: F-STWR can significantly improve STWR's capability of processing large-scale spatiotemporal data and is tested in a High-Performance Computing environment with a total number of 204,611 observations in 19 years.
4 citations
08 Aug 2022
TL;DR: A Bayesian neural network (BNN) ensembling method, which combines climate models within a Bayesian model averaging framework, to improve the predictive capability of model ensembles, is proposed and applied to an ensemble of CMIP6 climate models for monthly precipitation prediction over the conterminous United States.
Abstract: Multimodel ensembling has been widely used to improve climate model predictions, and the improvement strongly depends on the ensembling scheme. In this work, we propose a Bayesian neural network (BNN) ensembling method, which combines climate models within a Bayesian model averaging framework, to improve the predictive capability of model ensembles. Our proposed BNN approach calculates spatiotemporally varying model weights and biases by leveraging individual models’ simulation skill, calibrates the ensemble prediction against observations by considering observation data uncertainty, and quantifies epistemic uncertainty when extrapolating to new conditions. More importantly, the BNN method provides interpretability about which climate model contributes more to the ensemble prediction at which locations and times. Thus, beyond its predictive capability, the method also brings insights and understanding of the models to guide further model and data development. In this study, we apply the BNN weighting scheme to an ensemble of CMIP6 climate models for monthly precipitation prediction over the conterminous United States. In both synthetic and real case studies, we demonstrate that BNN produces predictions of monthly precipitation with higher accuracy than three baseline ensembling methods. BNN can correctly assign a larger weight to the regions and seasons where the individual model fits the observation better. Moreover, its offered interpretability is consistent with our understanding of localized climate model performance. Additionally, BNN shows an increasing uncertainty when the prediction is farther away from the period with constrained data, which appropriately reflects our predictive confidence and trustworthiness of the models in the changing climate.
1 citations
TL;DR: In this paper , a Bayesian neural network (BNN) ensembling method was proposed to improve the predictive capability of model ensembles by calculating spatiotemporally varying model weights and biases by leveraging individual models' simulation skill, calibrating the ensemble prediction against observations by considering observation data uncertainty, and quantifying epistemic uncertainty when extrapolating to new conditions.
Abstract: Multimodel ensembling has been widely used to improve climate model predictions, and the improvement strongly depends on the ensembling scheme. In this work, we propose a Bayesian neural network (BNN) ensembling method, which combines climate models within a Bayesian model averaging framework, to improve the predictive capability of model ensembles. Our proposed BNN approach calculates spatiotemporally varying model weights and biases by leveraging individual models' simulation skill, calibrates the ensemble prediction against observations by considering observation data uncertainty, and quantifies epistemic uncertainty when extrapolating to new conditions. More importantly, the BNN method provides interpretability about which climate model contributes more to the ensemble prediction at which locations and times. Thus, beyond its predictive capability, the method also brings insights and understanding of the models to guide further model and data development. In this study, we design experiments using an ensemble of CMIP6 climate model simulations to illustrate the BNN ensembling method's capability with respect to prediction accuracy, interpretability, and uncertainty quantification (UQ). We demonstrate that BNN can correctly assign larger weights to the regions and seasons where the individual model fits the observation better. Moreover, its offered interpretability is consistent with our understanding of localized climate model performance. Additionally, BNN shows an increasing uncertainty when the prediction is farther away from the period with constrained data, which appropriately reflects our trustworthiness of the models in the changing climate.
1 citations
TL;DR: Wang et al. as discussed by the authors developed a spatiotemporally weighted intelligent method based on a geographically and temporally neural network weighted regression (GTNNWR) model, a Data-Interpolating Empirical Orthogonal Functions (DINEOF), and satellite observations.
References
More filters
Proceedings Article•
01 Jan 1973
TL;DR: The classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion to provide answers to many practical problems of statistical model fitting.
Abstract: In this paper it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion. This observation shows an extension of the principle to provide answers to many practical problems of statistical model fitting.
18,539 citations
01 Jan 1973
TL;DR: In this paper, it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion.
Abstract: In this paper it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion. This observation shows an extension of the principle to provide answers to many practical problems of statistical model fitting.
15,424 citations
TL;DR: Robust locally weighted regression as discussed by the authors is a method for smoothing a scatterplot, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i, y i ) is large if x i is close to x k and small if it is not.
Abstract: The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for smoothing a scatterplot, (x i , y i ), i = 1, …, n, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i , y i ) is large if x i is close to x k and small if it is not. A robust fitting procedure is used that guards against deviant points distorting the smoothed points. Visual, computational, and statistical issues of robust locally weighted regression are discussed. Several examples, including data on lead intoxication, are used to illustrate the methodology.
10,225 citations
Book•
01 Jan 1991TL;DR: In this paper, the authors present a survey of statistics for spatial data in the field of geostatistics, including spatial point patterns and point patterns modeling objects, using Lattice Data and spatial models on lattices.
Abstract: Statistics for Spatial Data GEOSTATISTICAL DATA Geostatistics Spatial Prediction and Kriging Applications of Geostatistics Special Topics in Statistics for Spatial Data LATTICE DATA Spatial Models on Lattices Inference for Lattice Models SPATIAL PATTERNS Spatial Point Patterns Modeling Objects References Author Index Subject Index.
8,631 citations
TL;DR: A Computer Movie Simulating Urban Growth in the Detroit Region as discussed by the authors was made to simulate urban growth in the city of Detroit, Michigan, United States of America, 1970, 1970.
Abstract: (1970). A Computer Movie Simulating Urban Growth in the Detroit Region. Economic Geography: Vol. 46, PROCEEDINGS International Geographical Union Commission on Quantitative Methods, pp. 234-240.
7,533 citations