  Type Ia supernovae (SNe Ia) are used as distance indicators to infer the
cosmological parameters that specify the expansion history of the universe.
Parameter inference depends on the criteria by which the analysis SN sample is
selected. Only for the simplest selection criteria and population models can
the likelihood be calculated analytically, otherwise it needs to be determined
numerically, a process that inherently has error. Numerical errors in the
likelihood lead to errors in parameter inference. This article presents toy
examples where the distance modulus is inferred given a set of SNe at a single
redshift. Parameter estimators and their uncertainties are calculated using
Monte Carlo techniques. The relationship between the number of Monte Carlo
realizations and numerical errors is presented. The procedure can be applied to
more realistic models and used to determine the computational and data
management requirements of the transient analysis pipeline.
