Bit disappointed after reading the Lombardi et al. paper (link) on spatial Poisson processes today for two reasons: 1) the discussion is limited to a very simplistic (not really as a stochastic process) description of the SPP, along with a simplistic application; and 2) there is no referencing at all to the extensive work on this topic in the applied and theoretical statistics literature. When writing a pedagogical paper (such as my PASA article on computing confidence intervals for the binomial) I think one should be sure to distinguish between new and old contributions, and to provide references to more advanced works for further reading. Especially where giving proofs or theorems, it’s important not to present old/trivial knowledge available in any graduate statistics textbook or wikipedia as if an original contribution. For instance, after Lombardi et al.’s ‘derivation’ of the formula given in their Appendix A I would expect them to then say something like: “This is the standard argument given in, e.g., textbook X.” and/or “This heuristic argument parallels the formal proof for general measure spaces given by, e.g., Classic paper A”.

In addition, I thought there’d already been hundreds of uses of the spatial point process in astronomy and cosmology (e.g. for mapping large scale structure and detecting galaxy clusters and filaments: a quick ADS search brings up works by Elmo Tempel, Tom Loredo, Shethadri Nadathur in just the past few months); many of which are far more complicated than that given in the present work. It would have been worth emphasising, I think, that the type of scenario considered in this paper is most unusual in its simplicity and to point to more realistic examples for further reading (e.g. where the underlying field takes a (log) Gaussian process prior with unknown covariance parameters). Some mention of marked point processes and even fractional Poisson processes would also have been nice: the former having been used before in astronomy, the latter not so much (perhaps with the exception of Sheth 1998).

The strangest thing (not really so strange if you know anything about academia) though is that the three authors of this paper are all tenured (I think two are professors) at pretty good institutions. It’s not like I’m calling out a bunch of Phd students or early postdocs here …

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