What world events are affecting you?

Are most real-world events Poisson processes?

• A few background points : It seems that when studying occurences of some events, scientists quite often model that as a Poisson process. Lots of phenomena are well-explained by a Poisson process (e.g. from Wikipedia : Number of road crashes in an area, Requests for individual documents on a web server) However I'm not sure that most events that are experienced every day by an average person are well modeled by a Poisson process. For instance, the event "I'm hungry" is probably not Poisson at all. In neuroscience/psychology, the "Gambler's fallacy" is the mistaken belief that (for instance) after a long run of successive heads in a toss coin, a tail is more likely to happen next ; which can be understood as a mistaken belief that there is autocorrelation or some kind of structure in the "signal", when there is not (just like in a Poisson process). Other such "sequential effects" are shown in other experimental setups. I'm interested in why people are subject to the gambler's fallacy. In this paper [1], the authors measure the spatial statistics of 3D images, ie they measure the distribution of real-world spatial features. They show that if you assume that people use that real-world distribution as a prior, you explain very well the errors they make in a length-estimating task. I'm wondering whether something similar can be done for temporal signals (as opposed to spatial signals). The hypothesis is that people incorrectly believe there is a temporal structure in a signal because they have a prior that tells them that signals usually have some kind of temporal structure. That prior would come from (or just be adapted to) the statistics of real-world events. Hence my question : do you think real-world events are in majority Poisson? "Real-world event" is ill-defined here. Radioactive particle emissions is a real-world event that can be modelled by Poisson process, but I'm more interested in events that are actually experienced by people. Any thought on any part of all this is more than welcome! [1] http://www.pnas.org/content/99/20/13184.full Related questions :

• Answer:

  I think few real world processes are Poisson. The Poisson process might work for some applications in physics but as soon as humans become involved, typically there is more variance than seen in a Poisson process. My research is looking at blood bank inventory policies. This is a tricky area because both demand and supply are stochastic and blood components are perishable. But guess what? Previous researchers all assume demand and supply are Poisson processes. I am convinced that the real world does not work that way and I have good evidence of this.  However in my field the assumption is made because it makes the math easier. The question I am trying to answer in my research is how does the maths have to change in order to generalise the inventory models so that any distribution can be used. Specifically, as long as you know the mean and standard deviation of demand and supply you should be able to optimise blood inventory models without knowing anything else about the underlying distributions. I have found a clue as to how I might approach this problem in a1957 paper by Herbert Scarf.