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Large scale astronomical surveys are going wider and deeper than ever before.However, astronomers, cosmologists and theorists continue to face the perennialissue that their data sets are often incomplete in magnitude space and must becarefully treated in order to avoid Malmquist bias, especially in the field ofsupernova cosmology. Historically, cosmological parameter inference insupernova cosmology was done using $\chi^2$ methodology; however, recent yearshave seen a rise in the use of Bayesian Hierarchical Models. In this paper wedevelop a Bayesian Hierarchical methodology to account for magnitude limitedsurveys and present a specific application to cosmological parameter inferenceand model selection in supernova cosmology.

A Bayesian approach to truncated data sets: An application to Malmquist bias in Supernova Cosmology