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