avivajpeyi commented 1 week ago

Data generation

We take a ~4 day long signal:

$$y(a,f,\dot{f}, t) = a \left( \sin \left( 2 \pi \left( f t + 0.5 \dot{f} t^2 \right) \right) \right)$$

with

A_TRUE = 1e-21
F_TRUE =  3e-3
FDOT_TRUE = 1e-8

and add a ~6hr gap in the middle.

We then take each 'chunk' of timeseries, zero-pad and WDM transform it (bottom plot is the PSD): gaped_data

Single parameter likelihood

I set up a small search range:

A_RANGE = [9e-22, 1e-20]
LN_F_RANGE = [LN_F_TRUE-0.2, LN_F_TRUE+0.2]
LN_FDOT_RANGE = [LN_FDOT_TRUE-0.2, LN_FDOT_TRUE+0.2]

and compute the likelihood, changing one parameter at a time:

a	f	fdot

MCMC

Seems like the MCMC is taking a while to converge... corner mcmc

avivajpeyi commented 1 week ago

Can we just wavelet transform the entire timeseries with the gap? -- Maybe this will be hard due to correlations in the noise.

When we have gaps in timedomain, we need noise covar matrix in timedomain.

We need to take into account the noise correlations in the wavelet domain.

avivajpeyi commented 1 week ago

apply window --> wdm, do it several times, compute covar matrix
only wdm transform the chunks of timeseries --> do it several times, check the correlation of the wavelet trnasforms

avivajpeyi commented 1 week ago

Nt, Nf = 4, 8 ND = 32

Wnm.flatten = [...] shape-> 32

Flattened Wnm and Wn'm' covar matrix --> 32x32

diagonal -- var diagonal elements -- 4x8 (use instead of PSD)
off-diagonals -- covars

We want to show that we can use the var (the diagonal)

Then we can take the flattened Wnm covariance matrix, and recast recast --> 4x8x??

if we want to use the FULL covar matrix: s covar s

avivajpeyi commented 1 week ago

estimate Wnm noise matrix when we have gaps
1. assume a window function (box function)
1. stitching noise

repeat 100s of times: noise --> from PSD take noise --> WDM transform with and without windows.

WDM without windows:

flatten WDM transform -- compute individual covariance and cross covariance
compute autocorrelation betweeen

WDM with window:

flattem WDM transform -- compute sample covariance

Compute magnitude of off-diagonal terms

avivajpeyi commented 4 days ago

Ollie has made some progress on this. See https://github.com/pywavelet/case_studies/compare/db6b90b...4e04dfd

He says:

You can see with the Cornish style noise (high red noise) that the MCMC will not converge properly if noise is included (with the gap). It works very well if you set the filter kwarg to true… that is, if we filter out that nasty red noise then we converge to the true parameters. Cool.

avivajpeyi commented 2 days ago

The MCMC doesnnt seem to be working with noise... Sadness...

Is the noise correct?