Estimating the statistical uncertainty due to spatially correlated noise in interferometric images

Interferometers (e.g. ALMA and NOEMA) allow us to obtain the detailed brightness distribution of astronomical sources in 3 dimensions (R.A., Dec., frequency). However, spatial correlation noise makes it difficult evaluate statistical uncertainty measured quantities significance results obtained. The properties interferometric image are fully characterized easily by autocorrelation function (ACF). We present method for (1) estimating due correlated spatially integrated flux spectra directly, (2) simulating perform a Monte Carlo simulation analyses, (3) constructing covariance matrix chi-square $\chi^2$ be used when fitting model an with noise, based on ACF. demonstrate example applications scientific data showing that ignoring can lead significant underestimation false detections/interpretations.