I'm writing a paper on uncertainty estimation—how you put an error bar on your measurement—and at the same time, Kate Storey-Fisher (NYU) and I are working on a new method for estimating the correlation function (of galaxies, say) that improves the precision (the error bar) on measurements.
In the latter project (large-scale structure), we are encountering some interesting conceptual things. For instance, if you make many independent measurements of something (a vector of quantities say) and you want to plot your mean measurement and an uncertainty, what do you plot? Standard practice is to use the square root of the diagonal entries of the covariance matrix. But you could instead plot the inverse square roots of the diagonal entries of the inverse covariance matrix. These two quantities are (in general) very different! Indeed we are taught that the former is conservative and the latter is not, but it really depends what you are trying to show, and what you are trying to learn. The standard practice tells you how well you know the correlation function in one bin, marginalizing out (or profiling) any inferences you have about other bins.
In the end, we don't care about what we measure at any particular radius in the correlation function, we care about the cosmological parameters we constrain! So Storey-Fisher and I discussed today how we might propagate our uncertainties to there, and compare methods there. I hope we find that our method does far better than the standard methods in that context!
Apologies for this rambling, inside-baseball post, but this is my research blog, and it isn't particularly intended to be fun, useful, or artistic!
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