Estimating statistics of sky brightness using radio interferometric observations

Radio interferometric data are used to estimate the sky brightness distributions in radio frequencies. Here we focus on estimators of the large-scale structure and the power spectrum of the sky brightness distribution inferred from radio interferometric observations and assess their efficacy using simulated observations of the model sky. We find that while the large-scale distribution can be unbiasedly estimated from the reconstructed image from the interferometric data, estimates of the power spectrum of the intensity fluctuations calculated from the image are generally biased. The bias is more pronounced for diffuse emission. The visibility based power spectrum estimator, however, gives an unbiased estimate of the true power spectrum. We conclude that for an observation with diffuse emission the reconstructed image can be used to estimate the large-scale distribution of the intensity, while to estimate the power spectrum, visibility based methods should be preferred.