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I am interested in applications of point processes in machine learning, so I have been studying the theory of point process. However, I cannot see advantage of the theory of point processes compared with the classical probability theory.

For examples, I know the points of a Poisson point process scatters uniformly on a given domain. But, I'm confused what is the difference between Poisson point processes and uniform distribution functions (especially on a bounded domain).

I have similar questions for not only Poisson point processes but other point processes. Take sample points according to a point process. Can we obtain a similar (random) point set via using a probability distribution function?

What is advantage of using the theory of point processes instead of using probability distribution functions in statistics and machine learning?

Thank you so much in advance.

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Machine learning is about finding a model for your data and sometime the Point process is a better model than uniform or normal probability distribution.

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