

Understanding Waiting Times Between Events in a Poisson Process - nicolewhite
http://nbviewer.ipython.org/github/nicolewhite/notebooks/blob/master/Poisson.ipynb

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chejazi
A similar model applies to analyzing Bitcoin blocks. The "event" in this case
is a block that is at its maximum capacity:
[https://www.reddit.com/r/Bitcoin/comments/38zww2/tom_harding...](https://www.reddit.com/r/Bitcoin/comments/38zww2/tom_harding_block_size_experiment_underway/)

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kylebrown
The Poisson process equation is actually in Satoshi's whitepaper. The 6-block
confirmation rule-of-thumb comes from it.

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mrcactu5
I am nervous he should first very from his server logs these visits are indeed
described by a Poisson process (which is very likely the case).

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nicolewhite
It's not from the server logs that I would verify this is a Poisson process;
it's from the intuitive understanding that these events occur independently
from each other and at a constant, known rate. This process also possesses the
necessary properties[1] of a Poisson process.

[1]
[http://en.wikipedia.org/wiki/Poisson_process#Definition](http://en.wikipedia.org/wiki/Poisson_process#Definition)

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mturmon
Of course, for many web sites, the events are not independent.

If I visit one page, I'm likely to visit several more. If I see an interesting
page, I'm likely to forward it to friends. If I happen to have 1M twitter
followers, my visit could spark a cascade of visits.

Unless your models of site visits are very good (good enough to verify
independence), you would need to examine logs to determine if effects like
those above kick you completely out of a domain where independence is a good
approximation.

Note, time-dependence (a non-constant but deterministic rate λ(t)), is usually
easy to cope with. Lack of independence is much harder, because then you are
left with Cox processes
([http://en.wikipedia.org/wiki/Cox_process](http://en.wikipedia.org/wiki/Cox_process))
and worse.

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nicolewhite
Those are good points. The event in question is not a simple user visit,
however. Let's say it's a particular user action that's a bit more involved,
e.g. filling out a form. The assumption here is that users fill out this form
independently from one another.

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mturmon
Ah, I just noticed you are the OP.

Sure, you have to start somewhere with any analysis, and Poisson is the place
to start. Anyone (like me) can then question independence assumptions from the
sidelines.

I was moved to speak up originally because a commenter referred to inspecting
the logs to verify the Poisson assumption, and in my experience, looking at
the data is always an excellent principle, and generally preferable to just
stopping at an intuitive understanding of the arrivals process.

