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In this survey, we present and compare different approaches to estimateMutual Information (MI) from data to analyse general dependencies betweenvariables of interest in a system. We demonstrate the performance difference ofMI versus correlation analysis, which is only optimal in case of lineardependencies. First, we use a piece-wise constant Bayesian methodology using ageneral Dirichlet prior. In this estimation method, we use a two-stage approachwhere we approximate the probability distribution first and then calculate themarginal and joint entropies. Here, we demonstrate the performance of thisBayesian approach versus the others for computing the dependency betweendifferent variables. We also compare these with linear correlation analysis.Finally, we apply MI and correlation analysis to the identification of the biasin the determination of the aerosol optical depth (AOD) by the satellite basedModerate Resolution Imaging Spectroradiometer (MODIS) and the ground basedAErosol RObotic NETwork (AERONET). Here, we observe that the AOD measurementsby these two instruments might be different for the same location. The reasonof this bias is explored by quantifying the dependencies between the bias and15 other variables including cloud cover, surface reflectivity and others.

Survey On The Estimation Of Mutual Information Methods as a Measure of Dependency Versus Correlation Analysis