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I am reading a heuristic model of a herding activity of some animals. The mathematical (heuristic) model that was developed understandably includes an error term to account for a little randomness/non-deterministic behavior that occurs in the activity being modeled.

I have searched the entire paper looking for an explanation on what that kind of error might be, or how it might be distributed. Unfortunately, it doesn't mention.

What kind of distribution to these things have? Are they normal or uniform? Or what else? Does it depend on the problem being modeled or there is a mathematically acceptable practice to just assume the distribution which these error terms are defined?

Your insights will be valuable.

cgo
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1 Answers1

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Formally speaking, the distribution can be anything.

Traditionally, normal, uniform, and poisson models are the most common. Measuring "error" itself is not something that can be done explicitly since (unless your problem has more information) since we could always say "oh theres just a better model out there with less error". That being said, given some model X, that outputs predictions $X_0, X_1 ... $ we can ask for the error of that specific model, by comparing the variance of the actual observations from our predictions.

To add to @Tin Phan's comment the idea behind Poisson models is that if some amount of error (lets a deviance of size K) has probability m. Then one naturally can guess that

a deviance of size nK has the same likelihood as m times (probability of deviance of size (n-1)k)

From here we recover the Poisson model. Which, put another way, arises whenever the likelihood of a certain amount of error F, is independent of any previously acquired error G.

It's a pretty simple model that arises very naturally in settings.

Sidharth Ghoshal
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