Erlang mixture modeling for Poisson process intensities

We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through increments of a cumulative intensity function which is modeled nonparametrically with a gamma process prior. Such model specification provides a novel extension of Erlang mixtures for density estimation to the intensity estimation setting. The prior model structure supports general shapes for the point process intensity function, and it also enables effective handling of the Poisson process likelihood normalizing term resulting in efficient posterior simulation. The Erlang mixture modeling approach is further elaborated to develop an inference method for spatial Poisson processes. The methodology is examined relative to existing Bayesian nonparametric modeling approaches, including empirical comparison with Gaussian process prior based models, and is illustrated with synthetic and real data examples.

Inverse modeling of SO₂ and NO_<i>x</i> emissions over China using multisensor satellite data – Part 2: Downscaling techniques for air quality analysis and forecasts

Top-down emission estimates provide valuable up-to-date information on pollution sources; however, the computational effort and spatial resolution of satellite products involved with developing these emissions often require them to be estimated at resolutions that are much coarser than is necessary for regional air quality forecasting. This work thus introduces several approaches to downscaling coarse-resolution (2∘×2.5∘) posterior SO2 and NOx emissions for improving air quality assessment and forecasts over China in October 2013. As in Part 1 of this study, these 2∘×2.5∘ posterior SO2 and NOx emission inventories are obtained from GEOS-Chem adjoint modeling with the constraints of OMPS SO2 and NO2 products retrieved at 50 km×50 km at nadir and ∼190km×50km at the edge of ground track. The prior emission inventory (MIX) and the posterior GEOS-Chem simulations of surface SO2 and NO2 concentrations at coarse resolution underestimate observed hot spots, which is called the coarse-grid smearing (CGS) effect. To mitigate the CGS effect, four methods are developed: (a) downscale 2∘×2.5∘ GEOS-Chem surface SO2 and NO2 concentrations to the resolution of 0.25∘×0.3125∘ through a dynamic downscaling concentration (MIX-DDC) approach, which assumes that the 0.25∘×0.3125∘ simulation using the prior MIX emissions has the correct spatial distribution of SO2 and NO2 concentrations but a systematic bias; (b) downscale surface NO2 simulations at 2∘×2.5∘ to 0.05∘×0.05∘ according to the spatial distribution of Visible Infrared Imaging Radiometer Suite (VIIRS) nighttime light (NL) observations (e.g., NL-DC approach) based on correlation between VIIRS NL intensity with TROPOspheric Monitoring Instrument (TROPOMI) NO2 observations; (c) downscale posterior emissions (DE) of SO2 and NOx to 0.25∘×0.3125∘ with the assumption that the prior fine-resolution MIX inventory has the correct spatial distribution (e.g., MIX-DE approach); and (d) downscale posterior NOx emissions using VIIRS NL observations (e.g., NL-DE approach). Numerical experiments reveal that (a) using the MIX-DDC approach, posterior SO2 and NO2 simulations improve on the corresponding MIX prior simulations with normalized centered root mean square error (NCRMSE) decreases of 63.7 % and 30.2 %, respectively; (b) the posterior NO2 simulation has an NCRMSE that is 17.9 % smaller than the prior when they are both downscaled through NL-DC, and NL-DC is able to better mitigate the CGS effect than MIX-DDC; (c) the simulation at 0.25∘×0.3125∘ using the MIX-DE approach has NCRMSEs that are 58.8 % and 14.7 % smaller than the prior 0.25∘×0.3125∘ MIX simulation for surface SO2 and NO2 concentrations, respectively, but the RMSE from the MIX-DE posterior simulation is slightly larger than that from the MIX-DDC posterior simulation for both SO2 and NO2; (d) the NL-DE posterior NO2 simulation also improves on the prior MIX simulation at 0.25∘×0.3125∘, but it is worse than the MIX-DE posterior simulation; (e) in terms of evaluating the downscaled SO2 and NO2 simulations simultaneously, using the posterior SO2 and NOx emissions from joint inverse modeling of both species is better than only using one (SO2 or NOx) emission from corresponding single-species inverse modeling and is similar to using the posterior emissions of SO2 and NOx emission inventories respectively from single-species inverse modeling. Forecasts of surface concentrations for November 2013 using the posterior emissions obtained by applying the posterior MIX-DE emissions for October 2013 with the monthly variation information derived from the prior MIX emission inventory show that (a) the improvements of forecasting surface SO2 concentrations through MIX-DE and MIX-DDC are comparable; (b) for the NO2 forecast, MIX-DE shows larger improvement than NL-DE and MIX-DDC; (c) NL-DC is able to better decrease the CGS effect than MIX-DE but shows larger NCRMSE; (d) the forecast of surface O3 concentrations is improved by MIX-DE downscaled posterior NOx emissions. Overall, for practical forecasting of air quality, it is recommended to use satellite-based observation already available from the last month to jointly constrain SO2 and NO2 emissions at coarser resolution and then downscale these posterior emissions at finer spatial resolution suitable for regional air quality modeling for the present month.

Inverse modeling of SO₂ and NO_<i>x</i> emissions over China using multi-sensor satellite data: 2. Downscaling techniques for air quality analysis and forecasts

Top-down emissions estimates provide valuable up-to-date information on pollution sources; however, the computational effort involved with developing these emissions often requires them to be estimated at resolutions that are much coarser than is necessary for regional air-quality forecasting. This work thus introduces several approaches to downscaling coarse-resolution (2° × 2.5°) posterior SO2 and NOx emissions (derived through inverse modeling in Part I of this study) for improving air quality assessment and forecasts over China in October 2013. The SO2 and NOx emission inverse modeling was conducted at the 2° × 2.5° resolution in Part I to save computational time. The prior emission inventory (MIX) as well as the posterior GEOS-Chem simulations of surface SO2 and NO2 concentrations at this resolution underestimate observed hot spots, which is called the Coarse-Grid Smearing (CGS) effect. To mitigate the CGS effect, four methods are developed: (a) downscale 2° × 2.5° GEOS-Chem surface SO2 and NO2 concentrations to the resolution of 0.25° × 0.3125° through a Dynamic Downscaling Concentration (MIX-DDC) approach, which assumes that the 0.25° × 0.3125° simulation using the prior MIX emissions has the correct spatial distribution of SO2 and NO2 concentrations but a systematic bias; (b) downscale surface NO2 simulations at 2° × 2.5° to 0.05° × 0.05° according to the spatial distribution of Visible Infrared Imaging Radiometer Suite (VIIRS) Nighttime Light observations (e.g., NL-DC approach) based on correlation between VIIRS NL intensity with TROPOMI NO2 observations; (c) Downscale posterior Emissions (DE) of SO2 and NOx to 0.25° × 0.3125° with the assumption that the prior fine-resolution MIX inventory has the correct spatial distribution (e.g., MIX-DE approach); and (d) downscale posterior NOx emissions using VIIRS NL observations (e.g., NL-DE approach). Numerical experiments reveal that: (a) using the MIX-DDC approach, posterior SO2 and NO2 simulations improve compared to the corresponding MIX prior simulations with normalized centered root mean square error (NCRMSE) decreases of 63.7 % and 30.2 %, respectively; (b) the NO2 simulation has an NCRMSE that is 17.9 % smaller than the prior NO2 simulation when they are both downscaled through NL_DC, and NL_DC is able to better mitigate the CGS effect than MIX-DDC; (c) the simulation at 0.25° × 0.3125° using the MIX-DE approach has NCRMSEs that are 58.8 % and 14.7 % smaller than the prior 0.25° × 0.3125° MIX simulation for surface SO2 and NO2 concentrations, respectively, but the RMSE from the MIX-DE posterior simulation is slightly larger than that from the MIX-DDC posterior simulation for both SO2 and NO2; (d) the NL-DE posterior NO2 simulation also improves on the prior MIX simulation at 0.25° × 0.3125°, but it is worse than the MIX-DE posterior simulation; (e) in terms of evaluating the downscaled SO2 and NO2 simulations simultaneously, using the posterior SO2 and NOx emissions from joint inverse modeling of both species is better than only using one (SO2 or NOx) emissions from corresponding single-species inverse modeling and is similar to using the posterior emissions for both SO2 and inventories from single-species inverse modeling. Forecasts of surface concentrations for November 2013 using the posterior emissions obtained by applying the posterior MIX-DE emissions for October 2013 with the monthly variation information derived from the prior MIX emission inventory show (a) the improvements of forecasting surface SO2 concentrations through MIX-DE and MIX-DDC are comparable; (b) for NO2 forecast, MIX-DE show larger improvement than NL-DE and MIX-DDC; (c) NL-DC is able to better decrease the CGS effect than MIX-DE, but shows larger NCRMSE. Overall, for practical forecasting of air quality, it is recommended to use satellite-based observation already available from the last month to jointly constrain SO2 and NO2 emissions at coarser resolution and then downscale these posterior emissions at finer spatial resolution suitable for regional air quality model for the present month.

A Comparative Analysis of Posterior Simulation Techniques in the Estimation of Bayesian Regression Model

En los últimos años, el desarrollo de varias técnicas de simulación posterior ha impulsado el campo de la econometría bayesiana, especialmente en trabajos aplicados. La distribución previa juega un papel dominante en el análisis bayesiano; los anteriores están destinados a reflejar la información que el investigador tiene antes de ver los datos. Esta investigación examinó la sensibilidad de los métodos de muestreo de Gibbs (GS) e Integración de Monte Carlo (MCI) a tres niveles diferentes de correlación en covarianza previa para conocer los efectos de la correlación variable en los métodos de simulación posterior al estimar los parámetros en un modelo de regresión lineal. Los tres niveles diferentes de correlación son: Correlación negativa (NC), correlación positiva (PC) y correlación cero (ZC). Los resultados mostraron que el MCI superó al GS en la mayoría de los casos y la precisión del MCI no depende del nivel de correlación, ya sea positivo o negativo, mientras que el GS se desempeñó mejor cuando se usó el nivel de correlación positivo como información en la covarianza previa que el uso de un nivel negativo de correlación. El uso de MCI en la inferencia bayesiana podría ser de importancia práctica para los profesionales.