Model selection and multi-model inference

One of the principal aims of cosmology is to identify the correct cosmological model, able to explain the available high-quality data. Determining the best model is a two-stage process. First, we must identify the set of parameters that we will allow to vary in seeking to fit the observations. As part of this process we need also to fix the allowable (prior) ranges that these parameters might take, most generally by providing a probability density function in the N-dimensional parameter space. This combination of parameter set and prior distribution is what we will call a model, and it should make calculable predictions for the quantities we are going to measure. Having chosen the model, the second stage is to…