this is for holding javascript data
Matthew Pitkin Fix to equation 6
almost 7 years ago
Commit id: c83c3acdeb14adec2020501126eacae331800b88
deletions | additions
diff --git a/To_draw_points_from_the__.tex b/To_draw_points_from_the__.tex
index 5818532..f9b4c86 100644
--- a/To_draw_points_from_the__.tex
+++ b/To_draw_points_from_the__.tex
...
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. The cdf function can be 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} e^{-\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 $\varepsilon$/$Q_{22}$).