3 ms·
Wouldn't a Random Number Generator be a case of causation not implying correlation?
by jobigoud 13y ago
Wouldn't a Random Number Generator be a case of causation not implying correlation?
- cheald 13y agoIf you're talking about PRNGs, then no - there is a very specific correlation between successive numbers in a PRNG.
- ogrisel 13y agoBut it's highly non-linear. They have an expected Pearson correlation of zero. Note: there are simple counter example of variables that have a Pearson correlation of 0 yet some non-linear dependency structure as in the 3rd row of the plot of: http://en.wikipedia.org/wiki/Correlation_and_dependence http://en.wikipedia.org/wiki/Correlation_and_dependence
- mistercow 13y agoIf the question is "does causation imply linear correlation", then the answer is obviously and trivially "no". But we don't need a PRNG to see that. Take a series of chutes whose entrances are lined up in a row, and whose exits are arranged in a circle. Now start dropping balls in the entrances and see where they end up. Obviously there is a causal relationship between where we drop the ball and where it lands, but it's not a linear correlation. But there's still a correlation.
- mistercow 13y agoIn this example, what variables are you talking about being causally related?
- ogrisel 13y agoThe integer seeds of the PRNG on hand and the first (or second or nth) generated pseudo random number on the other hand.
- mistercow 13y agoI guess an even more obvious case would be a cryptographic hash, with the variables being the input and the output. But in this case still there is a correlation. In fact, the existence of the correlation is trivial to see: after a known transformation (the PRNG/hash itself) the correlation becomes linear.
- tel 13y agoConstant, even.