The rapid growth of astronomical data sets, coupled with the complexity of the questions scientists seek to answer with these data, creates an increasing need for the utilization of advanced statistical inference methods in astrophysics. Here, focus is placed on situations in which the underlying objective is the estimation of cosmological parameters, the key physical constants that characterize the Universe. Owing to the complex relationship between these parameters and the observable data, this broad inference goal is best divided into three stages. The primary objective of this article is to describe these stages and thus place into a coherent framework the class of inference problems commonly encountered by those working in this field. Examples of such inference challenges are presented.


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