scholarly journals Estimating model evidence using ensemble‐based data assimilation with localization – The model selection problem

2019 ◽  
Vol 145 (721) ◽  
pp. 1571-1588
Author(s):  
Sammy Metref ◽  
Alexis Hannart ◽  
Juan Ruiz ◽  
Marc Bocquet ◽  
Alberto Carrassi ◽  
...  
Keyword(s):  
Model Selection ◽  
Data Assimilation ◽  
Selection Problem ◽  
Model Evidence ◽  
Model Selection Problem

scholarly journals Bayesian uncertainty quantification in aerosol optical depth retrieval applied to TROPOMI measurements

2021 ◽  
Author(s):  
Anu Kauppi ◽  
Antti Kukkurainen ◽  
Antti Lipponen ◽  
Marko Laine ◽  
Antti Arola ◽  
...  
Keyword(s):  
Model Selection ◽  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Bayesian Model Averaging ◽  
Forward Model ◽  
Selection Problem ◽  
Aerosol Model ◽  
Model Discrepancy ◽  
Aerosol Types ◽  
Model Selection Problem

Abstract. We present here an aerosol model selection based statistical method in Bayesian framework for retrieving atmospheric aerosol optical depth (AOD) and pixel-level uncertainty. Especially, we focus on to provide more realistic uncertainty estimate by taking into account a model selection problem when searching for the solution by fitting look-up table (LUT) models to a satellite measured top-of-atmosphere reflectance. By means of Bayesian model averaging over the best-fitting aerosol models we take into account an aerosol model selection uncertainty and get also a shared inference about AOD. Moreover, we acknowledge model discrepancy, i.e. forward model error, arising from approximations and assumptions done in forward model simulations. We have estimated the model discrepancy empirically by a statistical approach utilizing residuals of model fits. We use the measurements from the TROPOspheric Monitoring Instrument (TROPOMI) onboard the Sentinel-5 Precursor in ultraviolet and visible bands, and in one wavelength band 675 nm in near-infrared, in order to study the functioning of the retrieval in a broad wavelength range. We exploit a fundamental classification of the aerosol models as weakly absorbing, biomass burning and desert dust aerosols. For experimental purpose we have included some dust type of aerosols having non-spherical particle shapes. For this study we have created the aerosol model LUTs with radiative transfer simulations using the libRadtran software package. It is reasonably straightforward to experiment with different aerosol types and evaluate the most probable aerosol type by the model selection method. We demonstrate the method in wildfire and dust events in a pixel level. In addition, we have evaluated in detail the results against ground-based remote sensing data from the AErosol RObotic NETwork (AERONET). Based on the case studies the method has ability to identify the appropriate aerosol types, but in some wildfire cases the AOD is overestimated compared to the AERONET result. The resulting uncertainty when accounting for the model selection problem and the imperfect forward modelling is higher compared to uncertainty when only measurement error is included in an observation model, as can be expected.

scholarly journals The Quality of the Covariance Selection through Detection Problem and AUC Bounds

2017 ◽  
Author(s):  
Navid Tafaghodi khajavi ◽  
Anthony Kuh
Keyword(s):  
Model Selection ◽  
Selection Problem ◽  
Upper And Lower Bounds ◽  
Detection Problem ◽  
Covariance Selection ◽  
Kl Divergence ◽  
Model Distribution ◽  
Original Distribution ◽  
Model Selection Problem

This paper considers the problem of quantifying the quality of a model selection problem for a graphical model. The model selection problem often uses a distance measure such as the Kulback-Leibler (KL) distance to quantify the quality of the approximation between the original distribution and the model distribution. We extend this work by formulating the problem as a detection problem between the original distribution and the model distribution. In particular, we focus on the covariance selection problem by Dempster, [1], and consider the cases where the distributions are Gaussian distributions. Previous work showed that if the approximation model is a tree, that the optimal tree that minimizes the KL divergence can be found by using the Chow-Liu algorithm [2]. While the algorithm minimizes the KL divergence it does not minimize other measures such as other divergences and the area under the curve (AUC). These measures all depend on the eigenvalues of the correlation approximation measure (CAM). We find expressions for KL divergence, log-likelihood ratio, and AUC as a function of the CAM. Easily computable upper and lower bounds are also found for the AUC. The paper concludes by computing these measures for real and synthetic simulation data.

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