![]() After reviewing the general mathematical formalism underlying matched filters, we study the statistics of the signal-to-noise with a set Monte Carlo mock observations, finding it to be well-described by a unit-variance Gaussian for signal-to-noise values of 6 and above, and quantify the magnitude of the optimization bias, for which we give an approximate expression that may be used in practice. Both aspects arise from the fact that the signal-to-noise is constructed through an optimization operation on noisy data, and hold even if the cluster signal is modelled perfectly well, no foregrounds are present, and the noise is Gaussian. In this work, we show that this observable is, in general, non-Gaussian, and that it suffers from a positive bias, which we refer to as optimization bias. In addition, they naturally provide an observable, the detection signal-to-noise or significance, which can be used as a mass proxy in number counts analyses of tSZ-selected cluster samples. Matched filters are routinely used in cosmology in order to detect galaxy clusters from mm observations through their thermal Sunyaev–Zeldovich (tSZ) signature.
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