this, we assume that the posterior is a multivariate normal distribution. In this case, the mutual information is: $$I(\Theta,X)\approx \frac{1}{2}\log_2\left(\frac{|A+C|}{|C|}\right),
\label{covar}$$ where $A$ is the covariance matrix of the prior, and $C$ is the covariance matrix of the posterior. This is a generalization of the single-variable case: $$I(\Theta,X)\approx \frac{1}{2}\log_2(1+\tau^2/\sigma^2),$$ where $\tau$ is the standard deviation of the prior, and $\sigma$ is the standard deviation of the posterior [@shannon48; @lindley1956]. If the probability distributions are Gaussians, Equation \[covar\] computes the mutual information exactly, and it should be a good approximation to mutual information for non-Gaussian distributions. We define this formula as the [*covariance matrix method*]{} for estimating the mutual information in the general case. This formula proceeds directly from the magnitude of the error bars, which is ultimately a figure of interest. In order to determine how accurate this method is for non-Gaussian distributions, we again average the results of many calculations from different random seeds.

JWST Capabilities {#JWST}
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JWST will have many observing modes for photometry, spectroscopy, and imaging. Of these, the spectroscopy modes are the most relevant for planetary atmosphere characterization via transit spectra since spectroscopy is needed to identify molecular features. As currently planned, JWST will have 