^{15}) cluster at z~1.1 by the South Pole Telescope, and its cosmological implications. Sections 2 and 3 give a nice description of the detection and observational methods, but I’m a little concerned about section 4. One of the key claims of this work is that “there is a 7% chance of finding a cluster at least as massive and at a redshift at least as high”.

Quantifying the extreme nature of a single variable, such as mass, would be a meaningful frequentist statement (although for those evangelical Bayesians out there, no such statement exists, but bear with me…). I’m just a bit concerned by this double condition which is enforced – using both mass and redshift.

For example, take a sample population of people in the UK, only one person can claim to be the shortest, and one the heaviest. But many can claim that ‘no one is both shorter and heavier than me’. Perhaps each city has one such person. We don’t know how many of these people there will be, or their statistical significance, until we better understand the relationship linking the two variables. What is really needed is a single measure, such as BMI in this analogy.

An appropriate statistic needs to invoke the mass-z relationship, (as depicted in Fig 5 of 1101.1290), which then allows us to compute whether one cluster is more extreme than another. This analysis will likely generate a result significantly greater than the quoted 7%, as it opens up a much larger area of parameter space.