I am trying to understand the heuristic connection between fitting a normal distribution to a dataset and the definition of what constitutes a random process.
If a normal distribution fits your data much better than other competing fits, then I presume that would constitute reasonable evidence that it is a random process. However, in practice, can we objectively say that this means that the process is indeed random?
More generally:
Can one ever truly prove (or disprove) a process to be random? Is there a set of conditions that need to be met for a process to be defined as random?
I was naturally led to wonder these questions after reading: The normal distribution is a common model of randomness