Speaker
Description
Cosmological observables often exhibit mild but significant deviations from Gaussianity, typically in the form of asymmetric tails. Using Gaussian likelihoods in such cases can therefore introduce systematic biases in parameter inference. We investigate the use of a skew-normal likelihood as a flexible alternative that captures these non-Gaussian features.
We focus on cosmic shear 2 point correlation function, a key weak lensing probe of the late-time large-scale structure, whose distribution has been shown to deviate from Gaussianity, particularly on larger scales. Using samples of data vectors from SLICS, which provide Euclid-like weak lensing simulations, we construct a pipeline to build a multivariate skew-normal likelihood model and then use it at the inference level.
This framework allows us to incorporate data points that are typically excluded under Gaussian assumptions due to their non-Gaussian distributions, thereby increasing the constraining power of the analysis. At the same time, the model naturally reduces to a Gaussian likelihood in the appropriate limit giving us a flexible pipeline to use it for the Gaussian parts of the data vectors. We further discuss how Gaussian noise can be consistently included at the likelihood level.
Our results show that for a fixed non-tomographic shear two-point correlation function with 20 data points, the parameter shift between Gaussian and skew-normal likelihoods is negligible ($< 0.1\sigma$ in $S_8$), indicating that Gaussian approximations remain adequate in this regime. However, when restricting the Gaussian analysis to a subset of 15 data points by excluding the most non-Gaussian elements, we observe a moderate shift ($\sim 0.6\sigma$ in $S_8$) relative to the skew-normal analysis using the full data vector. This demonstrates that the skew-normal likelihood enables the consistent inclusion of mildly non-Gaussian data points that would otherwise be discarded, leading to improved parameter constraints. In this setup, we find a $\sim 9 \%$ reduction in $S_8$ uncertainties. The skew-normal framework is expected to become increasingly important for larger and more non-Gaussian data vectors, such as those arising in tomographic analyses.