Update Additional Review (marginalization over joint population+EoS uncertainty) authored by Reed Essick's avatar Reed Essick
...@@ -35,7 +35,7 @@ The new version of the code relies on the user to specify the draw probability, ...@@ -35,7 +35,7 @@ The new version of the code relies on the user to specify the draw probability,
The previous version of the code implemented population priors by reweighing single-event PE samples. This was done within [this code block](https://git.ligo.org/reed.essick/mmax-model-selection/-/blob/c8b0d297d11b0a350c23ee44832d24b899729d8f/bin/mmax-model-selection#L227-270). Importantly, we see that the total weight for each PE sample was computed as the sum of population priors (implicit from [this block](https://git.ligo.org/reed.essick/mmax-model-selection/-/blob/c8b0d297d11b0a350c23ee44832d24b899729d8f/bin/mmax-model-selection#L263-270)). That sum was then normalized by the default PE prior [here](https://git.ligo.org/reed.essick/mmax-model-selection/-/blob/c8b0d297d11b0a350c23ee44832d24b899729d8f/bin/mmax-model-selection#L279). This means the overall weight assigned to each PE sample was The previous version of the code implemented population priors by reweighing single-event PE samples. This was done within [this code block](https://git.ligo.org/reed.essick/mmax-model-selection/-/blob/c8b0d297d11b0a350c23ee44832d24b899729d8f/bin/mmax-model-selection#L227-270). Importantly, we see that the total weight for each PE sample was computed as the sum of population priors (implicit from [this block](https://git.ligo.org/reed.essick/mmax-model-selection/-/blob/c8b0d297d11b0a350c23ee44832d24b899729d8f/bin/mmax-model-selection#L263-270)). That sum was then normalized by the default PE prior [here](https://git.ligo.org/reed.essick/mmax-model-selection/-/blob/c8b0d297d11b0a350c23ee44832d24b899729d8f/bin/mmax-model-selection#L279). This means the overall weight assigned to each PE sample was
```math ```math
w_i = \frac{\sum_p p(\theta_i)|\Lambda_p)}{p(\theta_i|\mathrm{default\ PE})} w_i = \frac{\sum_p p(\theta_i|\Lambda_p)}{p(\theta_i|\mathrm{default\ PE})}
``` ```
This implies that the total sum would be This implies that the total sum would be
... ...
......