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I've come here to hopefully resolve an issue that cropped up in a debate with a friend.

We were discussing weather patterns and chaos theory was brought up.

My understanding of chaos theory is that it is a way of explaining behavior of certain deterministic systems aka deterministic chaos. A bit of further reading seemed to show that chaos theory was now being applied to stochastic systems as well although I'm not really sure I understand this at all, if someone could give me something insight into this it would be appreciated.

My question really boils down to something quite simple though, what does chaos theory have to do with statistics? I feel that could well be a stupid question but it was raised and now I've managed to confused myself so I decided to turn to this forum.

Do we use statistical methods when applying chaos theory? I know its applied in economics, biology etc, how? Are there any good resources about these applications? I can find a few papers dotted about but they tend to require more background understanding than I feel I possess on the matter.

I'm asking in the statistics section as really that is the main problem I'm having, my friend insists they are linked but failed to provide any evidence, dismissing me as 'not understanding chaos theory' when I said I didn't see how statistics had anything to do with it.

I suppose as a supplemental question, what statistical methods are used when it comes to macroscopic weather patterns?

If anyone could shine some light on this I would be very appreciative.