Stochastic
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The JC’s amateur guide to systems theory™
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Stochastic
/stəˈkæstɪk/ (adj.)
Of an independent event, to be random: to have a calculable probability of occurring that is less than one and greater than zero. To be predictable by reference to probability only.
To qualify as a random distribution, events must be independent, each value must have a non-negative value, and the value of all events must add to 1. There must be a finite possible number of events.
Compare with deterministic (describing an event that is precisely predictable, such that it has a probability of 1) and uncertain (describing an event which is not independent or where controlling conditions are incomplete or unknown such that you cannot assign a probability at all.
Examples
Tossing a coin or rolling dice is stochastic: there are discrete outcomes, each of them is equally likely, but it is impossible to know which will come up in a given instance. Nonetheless, you know the probability of a given outcome exactly.
The next word uttered by a conscious human is neither deterministic not stochastic. It is not governed by, or explainable in terms of, probabilities.
The price of a stock market index at a point in the future seems stochastic, in that it must be a number and that number must be between zero and the total value of all issued currency in the world, but it isn’t. You can’t assign probabilities to dependent events controlled by human agency, as David “25-Sigma-Several Days-In-A-Row” Viniar would — probably? — tell you. So it really isn’t stochastic.
What Elon Musk is going to say on Twitter tomorrow is uncertain. There is no way of predicting it, or even assigning a probability to it. It is not even random.