Likelihood products from delensing likelihood presented in Han et al. 2020

Product Name
Delensed Parameter Shifts Covariance


Parameter Shift Covmatrix

This file includes the parameter shift covariance matrix. The covariance matrix is described in Han et al.

Parameter-shift is defined as the difference in a parameter estimated from lensed spectra and from delensed spectra. The dimension of this matrix is 20x20 for 20 free parameters analyzed in Han et al (6 LCDM parameters + 14 foreground parameters). The covariance is calculated from the best-fit parameters from 300 simulated lensed and delensed spectra on ACTPol DR4 D56 patch.

The parameters are ordered as follows from the first to the last column.

'a_tsz_act', 'a_ksz_act', 'xi_act', 'a_d_act', 
'a_s_act', 'a_c_act', 'a_g_act', 'a_tps_act', 'a_ps_act',
'a_gte_act', 'a_gee_act', 'beta_c_act', 'yp1_act', 'yp2_act'

See the accompanying image file to see what each *_act parameter represents.

Since we calculate the covariance matrix with a finite number of simulations, the estimation of the inverse of the covariance is biased. We correct for this bias using the equation (17) in Hartlap et al (https://arxiv.org/abs/astro-ph/0608064). In particular, throughout Han et al, we multiply the inverse of the parameter shift covariance matrix with a factor of (300-20-2)/(300-1).

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