ture, quantifying how the shape of the reconstructed temperature curve is related to the actual temperature series is difficult.

Ensembles of Reconstructions

One approach to depicting the uncertainty in the reconstructed temperature series is already done informally by considering a sample, or ensemble, of possible reconstructions. By graphing different approaches or variants of a reconstruction on the same axes, such as Figure S-1 of this report, differences in variability and trends can be appreciated. The problem with this approach is that the collection of curves cannot be interpreted as a representative sample of some population of reconstructions. This is also true of the 64 variants in Bürger and Cubasch (2005). The differences in methodology and datasets supporting these reconstructions make them distinct, but whether they represent a deliberate sample from the range of possible temperature reconstructions is not clear. As an alternative, statistical methods exist for generating an ensemble of temperature reconstructions that can be interpreted in the more traditional way as a random sample. Although this requires additional statistical assumptions on the joint distribution of the proxies and temperatures, it simplifies the interpretation of the reconstruction. For example, to draw inferences about the maximum values in past temperatures, one would just form a histogram of the maxima in the different ensemble members. The spread in the histogram is a rigorous way to quantify the uncertainty in the maximum of a temperature reconstruction.

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