Modeling fine-grained spatio-temporal pollution maps with low-cost sensors.

The use of air quality monitoring networks to inform urban policies is critical especially where urban populations are exposed to unprecedented levels of air pollution. High costs, however, limit city governments' ability to deploy reference grade air quality monitors at scale; for instance, only 33 reference grade monitors are available for the entire territory of Delhi, India, spanning 1500 sq km with 15 million residents. In this paper, we describe a high-precision spatio-temporal prediction model that can be used to derive fine-grained pollution maps. We utilize two years of data from a low-cost monitoring network of 28 custom-designed low-cost portable air quality sensors covering a dense region of Delhi. The model uses a combination of message-passing recurrent neural networks combined with conventional spatio-temporal geostatistics models to achieve high predictive accuracy in the face of high data variability and intermittent data availability from low-cost sensors (due to sensor faults, network, and power issues). Using data from reference grade monitors for validation, our spatio-temporal pollution model can make predictions within 1-hour time-windows at 9.4, 10.5, and 9.6% Mean Absolute Percentage Error (MAPE) over our low-cost monitors, reference grade monitors, and the combined monitoring network respectively. These accurate fine-grained pollution sensing maps provide a way forward to build citizen-driven low-cost monitoring systems that detect hazardous urban air quality at fine-grained granularities.

Robust inference in the negative binomial regression model with an application to falls data.

A popular way to model overdispersed count data, such as the number of falls reported during intervention studies, is by means of the negative binomial (NB) distribution. Classical estimating methods are well-known to be sensitive to model misspecifications, taking the form of patients falling much more than expected in such intervention studies where the NB regression model is used. We extend in this article two approaches for building robust M-estimators of the regression parameters in the class of generalized linear models to the NB distribution. The first approach achieves robustness in the response by applying a bounded function on the Pearson residuals arising in the maximum likelihood estimating equations, while the second approach achieves robustness by bounding the unscaled deviance components. For both approaches, we explore different choices for the bounding functions. Through a unified notation, we show how close these approaches may actually be as long as the bounding functions are chosen and tuned appropriately, and provide the asymptotic distributions of the resulting estimators. Moreover, we introduce a robust weighted maximum likelihood estimator for the overdispersion parameter, specific to the NB distribution. Simulations under various settings show that redescending bounding functions yield estimates with smaller biases under contamination while keeping high efficiency at the assumed model, and this for both approaches. We present an application to a recent randomized controlled trial measuring the effectiveness of an exercise program at reducing the number of falls among people suffering from Parkinsons disease to illustrate the diagnostic use of such robust procedures and their need for reliable inference.