deletions | additions       diff --git a/Ultimately_we_are_interested_in__.tex b/Ultimately_we_are_interested_in__.tex  index 46216d0..deb5a3a 100644  --- a/Ultimately_we_are_interested_in__.tex  +++ b/Ultimately_we_are_interested_in__.tex 
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Ultimately, we are interested in converting the density of observed parameters to the density of actual parameters, and Equation \ref{eqn:convert_from_actual_to_observed_density} provides a way to do that. The equation involves an integral over $b$, which, given $\Gamma_{\rm obs}$ and $P_{\rm obs}$, represents a fixed curve in $\Gamma_{\rm act}-P_{\rm act}$. In other words, $\Gamma_{\rm obs}$ and $P_{\rm obs}$ define a locus of points for $\Gamma_{\rm act}$ and $P_{\rm act}$, and the integral over $b$ involves traveling along the locus from the point $(\Gamma_{\rm act}, P_{\rm act}) = (\Gamma_{\rm obs}, P_{\rm obs})$ up to $(\Gamma_{\rm obs} \left( P_{\rm obs}/P_{\rm max} \right)^{1/2}, P_{\rm max})$  Figure \ref{fig:integration_path} illustrates  \begin{eqnarray}  \label{eqn:convert_from_observed_to_actual_density}