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......@@ -37,14 +37,33 @@ This is the home page for the review of the detection of non-quadrupole modes us
## Review statements
We have reviewed the implementation of 'search of higher modes in the gravitational wave strain assuming the detection of 22 mode' using time-frequency map of the data. The method was introduced in (https://arxiv.org/abs/1910.04565) and presented in [R&D call 2019-08-19](https://dcc.ligo.org/G1901496). The brief summary of analysis is as below:
1. Extract the parameters of the event from PE summary page or GraceDB.
2. Construct the time-frequency map (by wavelet transform using Morlet wavelet: Details: ) of the whitened data surroundings the event. The wavelet used in the analysis is different from the one described in the method paper. Details on the wavelet tranform is summarised [here](https://git.ligo.org/soumen.roy/o3inspiralhom/-/wikis/uploads/bf743a417b1494559a3613d8d3aed501/cwt_doc.pdf).
3. Collect the energies in the pixels along various scaled 22-track. Especially, the arbitrary track is defined as $`f_{\alpha}(t) = \alpha f_{22}(t)`$, where the 22-track is generated using parameters obtained from PE/GraceDB. The summed energy along the $`f_{\alpha}(t)`$ track is defined as $`Y(\alpha)`$.
4. The template model $`S(\alpha)`$ is constructed using the same mass-spin parameters.
5. Two consecutive points in $`Y(\alpha)`$ are highly correlated; thereby, the covariance matrix is necessary for hypothesis testing. The covariance matric is computed using the off-source data surrounding the event.
6. Finally, we defined a statistic ($`\beta`$) for detecting the higher-order modes from the inspiral part of the signal. For pure Gaussian noise case, the statistic $`\beta`$ follows a Gaussian distribution with zero mean and unit variance when no gravitational wave presents in the data, i.e., $`p(\beta \mid \mathcal{H}_0 ) \sim \mathcal{N}(0, 1)`$. However, $`p(\beta \mid \mathcal{H}_0 )`$ need not to be pure Gaussian for real LIGO data.
The python implementation of the analysis cam be found [here](). We have done a line-by-line code review here.
| Script | Short description | Status | git hash | Comment | final sign-off |
| ------ | ----------------- | ------ | -------- | ------- | -------------- |
| utils.py | Content: Class MiscellaneousUtils: Main Class for the analysis , Function NegativeLogLikelihoodRatio: Used for maximizing the LLR over unknown overall amplitudes of the template model of each 'm' mode. | Done | | |Nathans:?, Haris:|
| noisebg.py | Tools for computing background distribution| Done | | |Nathans:?, Haris: |
| calndm.py | Tools to obtain best central frequency of the wavelet, by maximizing power along 22 modes track| Done | | |Nathans:?, Haris: |
| inspiralhom_analysis.py | Stand-alone python script to perform the analysis on an event. | | | |Nathans:?, Haris: |
# Investigations for code review
| Reviewer| Task | Status | Link to review material | Persons Responsible | Comment | final sign-off |
| ------ | ------ |--------|-------------------------|---------------------|---------------|----------------|
| [Nathan K. Johnson-McDaniel](https://git.ligo.org/nathan-johnson-mcdaniel) | Choise on ending frequency of the $`22-`$mode track | To be updated | [Link](https://git.ligo.org/soumen.roy/o3inspiralhom/wikis/overelap33) | Soumen | Haris: for S190412m the overlaps between S(\alpha) for 22 and 33 modes are less than 3% for ending frequencies<0.6f_ISCO. Need to check for S190814bv also. | Nathan: ?, Haris:? |
| [Nathan K. Johnson-McDaniel](https://git.ligo.org/nathan-johnson-mcdaniel) | Choise on ending frequency of the $`22-`$mode track | To be updated | [Link](https://git.ligo.org/soumen.roy/o3inspiralhom/wikis/overelap33) | Soumen | Haris: for S190412m the overlaps between $`S(\alpha)`$ for 22 and 33 modes are less than 3% for ending frequencies<0.6f_ISCO. Need to check for S190814bv also. | Nathan: ?, Haris:? |
| [Haris K](https://git.ligo.org/haris-k), [Nathan K. Johnson-McDaniel](https://git.ligo.org/nathan-johnson-mcdaniel) | Comparison of PSDs between Welch and BayesLine | DONE | [Link](https://git.ligo.org/soumen.roy/o3inspiralhom/wikis/PSDs-comparison) | Soumen | Haris: PSDs looks consistant for detection purposes. | Nathans:?, Haris:**OK** |
| [Haris K](https://git.ligo.org/haris-k), [Nathan K. Johnson-McDaniel](https://git.ligo.org/nathan-johnson-mcdaniel) | Study on choice of deltaT and deltaF | To be updated | [Link](https://git.ligo.org/soumen.roy/o3inspiralhom/-/wikis/Study-on-choice-of-deltaT-and-deltaF) | Soumen | Haris: Y(\alpha) is defined as the sum of energy content of the pixels along the $a\lpha$ track. Thus it will depend on the pixel size. However the final $\beta$ will be independent of the choice of pixel size. Further for sample rates<=4KHz, the the spectrograms seems to be consistent for various choices of sampling rate. The analysis is restricted to sample rates<=4KHz | Nathan: ?, Haris:? |
| [Haris K](https://git.ligo.org/haris-k), [Nathan K. Johnson-McDaniel](https://git.ligo.org/nathan-johnson-mcdaniel) | Study on $`p-`$value | Done | [Link](https://git.ligo.org/soumen.roy/o3inspiralhom/-/wikis/Study-on-p-value) | Soumen | Nathan: ?, Haris: Extrapolation of $P(\beta\|H_0)$ doesn't seem to be a good idea. Will use background samples to quote an upper bound on *p*-value | Nathan: ?, Haris: **OK** |
| [Haris K](https://git.ligo.org/haris-k), [Nathan K. Johnson-McDaniel](https://git.ligo.org/nathan-johnson-mcdaniel) | Study on choice of deltaT and deltaF | To be updated | [Link](https://git.ligo.org/soumen.roy/o3inspiralhom/-/wikis/Study-on-choice-of-deltaT-and-deltaF) | Soumen | Haris: $`Y(\alpha)`$ is defined as the sum of energy content of the pixels along the $`\alpha`$ track. Thus it will depend on the pixel size. However the final $`\beta`$ will be independent of the choice of pixel size. Further for sample rates<=4KHz, the the spectrograms seems to be consistent for various choices of sampling rate. The analysis is restricted to sample rates<=4KHz | Nathan: ?, Haris:? |
| [Haris K](https://git.ligo.org/haris-k), [Nathan K. Johnson-McDaniel](https://git.ligo.org/nathan-johnson-mcdaniel) | Study on $`p-`$value | Done | [Link](https://git.ligo.org/soumen.roy/o3inspiralhom/-/wikis/Study-on-p-value) | Soumen | Nathan: ?, Haris: Extrapolation of $`P(\beta\|H_0)`$ doesn't seem to be a good idea. Will use background samples to quote an upper bound on *p*-value | Nathan: ?, Haris: **OK** |
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