Review.md

@@ -8,4 +8,28 @@
 
 - [September 20, 2022](Review-meeting-Sep.-20,-2022)
 
-# Tests
+# Introduction
\ No newline at end of file
+
+Migrating LIV analysis to bilby and making it compatible with Asimov
+
+## Parametrizations
+1. Parametrization in log10_lambda_eff, used in O3 and implemented in lal_simulation
+```math
+\delta \Phi_{\alpha}(f)=sign(A_\alpha) \begin{cases}\frac{\pi D_L}{\alpha-1}\lambda_{A,eff}^{\alpha-2}(\frac f c)^{\alpha-1} & \alpha  \neq 1\\\frac{\pi D_L}{\lambda_{A,eff}}\ln(\frac{\pi G \mathcal{M}f}{c^3})& \alpha = 1\end{cases} 
+```
+
+
+2. Parametrization in A_eff, implemented in bilby as phase correction to the waveform
+
+```math
+\delta \Phi_{\alpha}(f)= -\frac{\pi D_L h^{\alpha-2}}{c}A_{\alpha,eff}(f )^{\alpha-1}
+```
+
+
+## Using the package
+
+To use the package for LIV testing in bilby:
+1. Choose the appropriate function in bilbyLIV/waveform.py as frequency_domain_source_model
+2. Choose bilbyLIV.conversion.generate_all_bbh_parameters (or bns) as generation function to generate A_alpha in the posterior samples
+3. In the prior, include a prior in A_eff (in peV^(2-alpha)). Additionaly include a delta prior in alpha (must be 0, 0.5, 1., 1.5, 2.5, 3.0, 3.5, 4.). Recommended prior is `A_eff = SymmetricLogUniform(name='A_eff', minimum=1e-24, maximum=1e-12, unit='$peV^{2-\\alpha}$', latex_label='$A_{eff}$')`
+