On Statistical Approaches to Generate Level 3 Products from Satellite Remote Sensing Retrievals

Comparison of new computational methods for spatial modelling of malaria

BACKGROUND

Geostatistical analysis of health data is increasingly used to model spatial variation in malaria prevalence, burden, and other metrics. Traditional inference methods for geostatistical modelling are notoriously computationally intensive, motivating the development of newer, approximate methods for geostatistical analysis or, more broadly, computational modelling of spatial processes. The appeal of faster methods is particularly great as the size of the region and number of spatial locations being modelled increases.

METHODS

This work presents an applied comparison of four proposed 'fast' computational methods for spatial modelling and the software provided to implement them-Integrated Nested Laplace Approximation (INLA), tree boosting with Gaussian processes and mixed effect models (GPBoost), Fixed Rank Kriging (FRK) and Spatial Random Forests (SpRF). The four methods are illustrated by estimating malaria prevalence on two different spatial scales-country and continent. The performance of the four methods is compared on these data in terms of accuracy, computation time, and ease of implementation.

RESULTS

Two of these methods-SpRF and GPBoost-do not scale well as the data size increases, and so are likely to be infeasible for larger-scale analysis problems. The two remaining methods-INLA and FRK-do scale well computationally, however the resulting model fits are very sensitive to the user's modelling assumptions and parameter choices. The binomial observation distribution commonly used for disease prevalence mapping with INLA fails to account for small-scale overdispersion present in the malaria prevalence data, which can lead to poor predictions. Selection of an appropriate alternative such as the Beta-binomial distribution is required to produce a reliable model fit. The small-scale random effect term in FRK overcomes this pitfall, but FRK model estimates are very reliant on providing a sufficient number and appropriate configuration of basis functions. Unfortunately the computation time for FRK increases rapidly with increasing basis resolution.

CONCLUSIONS

INLA and FRK both enable scalable geostatistical modelling of malaria prevalence data. However care must be taken when using both methods to assess the fit of the model to data and plausibility of predictions, in order to select appropriate model assumptions and parameters.

A review of datasets and methods for deriving spatiotemporal distributions of atmospheric CO2

As the most abundant greenhouse gas, atmospheric carbon dioxide (CO₂) is considered one of the main attributors to climate change. Atmospheric CO₂ concentrations can be measured by ground-based monitoring networks, mobile monitoring campaigns, and carbon-observing satellites. However, the worldwide ground-based monitoring networks are composed of sparsely distributed sites and are inadequate to represent the spatiotemporal distributions of CO₂. Satellite-based remote sensing features repeated, long-term, and large-scale measurements, so it plays a crucial role in monitoring the global distributions of atmospheric CO₂. However, due to the presence of heavy clouds (or aerosols) and the limitation of satellite orbiting tracks, there exist large amounts of missing data in satellite retrievals. Various methods, including chemical transport models (CTMs), geostatistical methods, and regression-based models, have been employed to derive full-coverage spatiotemporal distributions of CO₂ based on the limited CO₂ measurements. This review summarizes the strengths and limitations of these methods. However, CTMs simulation results can have high uncertainty due to imperfect knowledge of the real world, and the interpolation accuracy of all geostatistical methods is limited by the large amount of data gaps in current satellite retrieved CO₂ products. To overcome these limitations, regression-based methods (especially machine learning models) have the ability to predict CO₂ with superior predictive performance, so this review also summarizes the framework of the machine learning approach. Leveraging the ongoing advancements of satellite instrumentation, the satellite-based CO₂ products have been improving dramatically in recent decades, and this review will describe and critically assess the advantages and disadvantages of the currently used systems in detail. For future improvements, we recommend the fusion of data from multiple satellite retrievals and CTMs by using machine learning algorithms in order to obtain even longer-term, larger-scale, finer-resolution, and higher-accuracy CO₂ datasets.

A Case Study Competition Among Methods for Analyzing Large Spatial Data

The Gaussian process is an indispensable tool for spatial data analysts. The onset of the "big data" era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low-rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics. Supplementary materials regarding implementation details of the methods and code are available for this article online.

ELECTRONIC SUPPLEMENTARY MATERIAL

Supplementary materials for this article are available at 10.1007/s13253-018-00348-w.