deletions | additions       diff --git a/To_draw_points_from_the__.tex b/To_draw_points_from_the__.tex  index 1d4bd1a..767cee7 100644  --- a/To_draw_points_from_the__.tex  +++ b/To_draw_points_from_the__.tex 
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To draw points from the Fermi-Dirac-like distribution in Eq.~\ref{eq:fermidirac} we would draw values uniformly between 0 and 1 and then for each value invert the cdf. Unfortunately the The  cdf functioncannot simply be inverted. However, the cdf can easily be computed over a fine grid of values and the corresponding $h_0$ value can be calculated via interpolation, or $h_0$  can be computed using a root finding algorithm. inverted to give  \begin{equation}  H_0 = -\sigma \log{}\left(-e^{-\mu/\sigma} + \left(1+e^{\mu/\sigma} \right)^{-C(H_0)} + e^{1-\mu/\sigma}\left(1+e^{\mu/sigma} \right)^{-C(H_0)} \right).  \end{equation}  It is definitely worth testing out this as a prior for the searches. I should also look into the Jacobian between this and a prior distribution as I might need that when thinking about using posterior samples of $h_0$ to work out the underlying distributions of $h_0$ (or $\varepsilon$/$Q_{22}$).