Edits to Poisson example in chapter 1

[CamDavidsonPilon]

From Alex Nelson (direct communication)

In chapter 1 when you describe the Poisson distribution, I have some suggestions.

First, your description of lambda could be improved. You should describe it as the "intensity" of the distribution, which can be seen if one derives it from the Binomial distribution Bin(n,p) taking n to infinity, provided we fix n*p = lambda.

Second, why not leave the aforementioned derivation as an exercise? (Or -- what I do in my notes -- is ask it as a question, then insist the reader make the attempt, and solve it in an example.)

[xcthulhu]

There's reason to doubt that texting behavior is correctly modeled with Poisson statistics at all [1].

Better examples (off the top of my head):

• Minute-by-minute photon counts for the Chandra high-energy space telescope for a given observation
• Minute-by-minute counts for a number of flies on a cow-pie

Those aren't very sexy though :(

[1] A.-L. Barabási, (2005). "The origin of bursts and heavy tails in human dynamics.". Nature 435 (7039): 207–211. arXiv:cond-mat/0505371. Bibcode:2005Natur.435..207B. doi:10.1038/nature03459. PMID 15889093

[CamDavidsonPilon]

I agree with your first statement, and in fact it is a poor model (the data's variance is too high ). Later I will reexamine the problem, show that it is a poor model, and propose a better model (negative-binomial)

[xcthulhu]

Well, I myself am curious how Barabási's model performs on real world data. He's certainly publicized it enough; There's his Nature paper, and he even wrote a book about it (Bursts [2010]).

AFAIK, nobody has ever carried out an analysis of his model in a Bayesian setting. I might be willing to help check it out for your book if you're down.

[CamDavidsonPilon]

Okay, I will try to implement it. It does look very interesting. Thanks for showing me this.