Anja Weyant, Chad Schafer, W. Michael Wood-Vasey
Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modelled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is increasing burden placed on adequate modelling; systematic errors in the model will dominate where previously these were swamped by statistical errors. For example, Gaussian distributions are an insufficient representation for errors in quantities like photometric redshifts. Likewise, it can be difficult to quantify analytically the distribution of errors that are introduced in complex fitting codes. Without a simple form for these distributions, it becomes difficult to accurately construct a likelihood function for the data as a function of parameters of interest. Approximate Bayesian Computation (ABC) provides a means of probing the posterior distribution when direct calculation of a sufficiently accurate likelihood is intractable. ABC allows one to bypass direct calculation of the likelihood but instead relies upon the ability to simulate the forward process that generated the data. These simulations can naturally incorporate priors placed on nuisance parameters, and hence these can be marginalized in a natural way. We present and discuss ABC methods in the context of supernova cosmology.
View original:
http://arxiv.org/abs/1206.2563
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