Robustness to Systematic Error for Future Dark Energy Probes

The Fisher matrix formalism outlined in Sect. 5.3 gives a useful methodology for predicting the error ellipses around the fiducial model on the parameters of interest for future proposed astrophysical probes of cosmology. One of the most common Figures of

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Robustness to Systematic Error for Future Dark Energy Probes

The Fisher matrix formalism outlined in Sect. 5.3 gives a useful methodology for predicting the error ellipses around the fiducial model on the parameters of interest for future proposed astrophysical probes of cosmology. One of the most common Figures of Merit (FoM) used as a metric for comparing proposed probes is the inverse area of the error ellipse derived from the Fisher matrix formalism [1, 2] which gives a measure of the expected statistical power or ability of a probe to be able to constrain the parameters of interest. Alternative FoMs in higher dimesnions are given by Huterer and Turner [3]–Mortonson et al. [7], and a more general Bayeisan approach to FoMs is given in [8]. The purpose of the FoM is to evaluate in advance the expected statistical power of future probes. Survey parameters can be adjusted in order to maximise the statistical power of a particular probe, and proposed probes can be ranked by their FoM. This ranking can then assist in the decision making process of how to allocate limited resources to get the best science return. One of the limitations of the inverse area FoM is that it does not take into consideration what would happen if either the current or future proposed probe were biased—these inverse area FoMs are evaluated at the fiducial model in parameter space. But what happens if the future proposed probe is biased, that is shifted somewhat in parameter space with respect to the fiducial model due to unforeseen systematic errors? How can we evaluate the possible impact of bias inducing systematic errors which shift the proposed probe with respect to the fiducial model? How can we quantify which probes are more or less robust to systematic errors? In order to address these questions and provide a method for quantifying the robustness to systematic errors of future proposed probes, we have extended the FoM formalism to give a new ‘Robustness’ statistic. In this chapter I first give an overview of the standard statistical FoM and then introduce our new Robustness FoM, discussing its properties with reference to a Gaussian linear model. I then present a case study in which I apply the Robustness FoM to two future dark energy probes, supernovae type Ia (SNe Ia) and Baryon Acoustic Oscillations (BAO). This chapter follows closely the paper March et al. [9].

M. C. March, Advanced Statistical Methods for Astrophysical Probes of Cosmology, Springer Theses, DOI: 10.1007/978-3-642-35060-3_8, © Springer-Verlag Berlin Heidelberg 2013

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8 Robustness to Systematic Error for Future Dark Energy Probes

8.1 Figures of Merit for Future Dark Energy Probes 8.1.1 Gaussian Linear Model Suppose there are two different dark energy probes, whose likelihood function is assumed to be Gaussian and is characterized by a Fisher matrix (i.e. inverse covariance matrix) L i (i = 1, 2), i.e.  Li () ≡ p(di |) =

Li0 exp

1 − (μi − )t L i (μi − ) 2

 (8.1)

where  are the parameters of interest and μi is the location of the maximum likelih