Eric Linder edited Appendix.tex  over 10 years ago

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\section{Cosmographic Accuracy}  {\bf [EL: I didn't understand the need for this whole appendix. All that seems to matter is $\sqrt{N}$. There's no need to concentrate on $H_0$. The sensitivities for all the cosmology parameters are shown in Fig.~1 of 1109.2592 ($H_0$ would be trivial as a horizontal line at 100 in this plot).]}  In this appendix we show how time delay precision can be approximately related to precision in cosmological parameters, thereby justifying the challenge requirements in that context.  We do so by considering the emulation of a joint inference of $H_0$ given a sample of $N$ observed strong lenses, each providing (for simplicity) a single measured time delay $\tilde{\Delta t}_i$. This $i^{\rm th}$ measurement is encoded in a contribution to the joint likelihood, which when written as a function of all the independently-obtained data $\mathbf{\tilde{\Delta t}}$ is the probability distribution