high value, and hence the model will have a high evidence value associated with it. However if the model is over-complex then there will be large regions of low likelihood within the prior volume, thus reducing the evidence value for this model, in agreement with Occam’s razor. This provides a mechanism to choose between competing models $\mathcal{M}_\rmn{j}$.

The SZ Likelihood
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The focus of this work is interferometric SZ data, which are assumed to have Gaussian distributed errors, and so have a likelihood that is expressed in the form given by Equation\[equation:gaussian\_likelihood\]. The SZ data consist of complex visibilities from the output of the correlator, which encode the Fourier transform of the product of the sky brightness and the primary beam of the instrument. The visibilities only sample the Fourier transform at discrete coordinates in the Fourier plane, defined by the configuration of the instrument antennas during the observation.

Errors in the SZ data originate from three main sources; the thermal noise, the intrinsic CMB anisotropy and radio point sources. The total covariance matrix is thus given by the sum of these individual components, $$\mathbfss{C}_\rmn{SZ} = \mathbfss{C}_\rmn{noise} + \mathbfss{C}_\rmn{CMB} + \mathbfss{C}_\rmn{sources}.$$ The thermal noise component originates from the instrument electronics, 