4 ms·

Correct me if I'm wrong, but surely in the scenario that you are Ashton Kutcher and tweet a link to your followers, the average inter-arrival time would decreas

by hassy 11y ago

Correct me if I'm wrong, but surely in the scenario that you are Ashton Kutcher and tweet a link to your followers, the average inter-arrival time would decrease but overall it would still be a Poisson process?

mturmon 11y ago
It would not be Poisson, because the arrivals are not statistically independent. Let's take a simpler case, where I have one follower who has a high probability of clicking links from my tweets, and there is a webpage that only I know about. I visit that page, tweet it, and an hour later, with high probability, my follower visits it. The event { I visit page } and the event { follower visits page } are not independent, and neither is the arrival process associated with it. In the extreme case, for large times, there are either zero visits to the link, or two, but never just one (obviously non-Poisson). The Kutcher example is just this, magnified. Independence is a very strong assumption, but it is often casually stated. Independence is what allows you to decompose a very complex process (all those arrivals) into their individual atomic events (a single arrival). Without invoking independence, you have a very complex task in relating how each of the N possible sources of events might relate to each other. It could be arbitrarily complex (e.g., some followers might only click a link if two people they're following like it, unless Ashton likes it, in which case they will never visit it, but if Colbert likes it, that will override Ashton).
- hassy 11y ago
  Thanks for taking the time to explain! I understand that each { follower visits page } is dependent on the { Ashton Kutcher tweets } event, but I still don't understand why events are not independent of each other, and why the N visits to the webpage in time period T from the tweet would not likely be described by a Poisson process. Not expecting an answer btw, just thinking out loud here. :)

by hassy 11y ago

mturmon 11y ago

It would not be Poisson, because the arrivals are not statistically independent. Let's take a simpler case, where I have one follower who has a high probability of clicking links from my tweets, and there is a webpage that only I know about. I visit that page, tweet it, and an hour later, with high probability, my follower visits it. The event { I visit page } and the event { follower visits page } are not independent, and neither is the arrival process associated with it. In the extreme case, for large times, there are either zero visits to the link, or two, but never just one (obviously non-Poisson). The Kutcher example is just this, magnified. Independence is a very strong assumption, but it is often casually stated. Independence is what allows you to decompose a very complex process (all those arrivals) into their individual atomic events (a single arrival). Without invoking independence, you have a very complex task in relating how each of the N possible sources of events might relate to each other. It could be arbitrarily complex (e.g., some followers might only click a link if two people they're following like it, unless Ashton likes it, in which case they will never visit it, but if Colbert likes it, that will override Ashton).

hassy 11y ago
Thanks for taking the time to explain! I understand that each { follower visits page } is dependent on the { Ashton Kutcher tweets } event, but I still don't understand why events are not independent of each other, and why the N visits to the webpage in time period T from the tweet would not likely be described by a Poisson process. Not expecting an answer btw, just thinking out loud here. :)