# The books always give the caveat “if independent”

I'm looking for statistics and probability books/resources that tackle dependant variables/events/etc. The real world is almost never iid.

I'm interested in the mathematics of solving problems that have dependence at their core.

PS. I'm at the end of an introductory statistics book (1-2 year university), and would like to gain deeper mathematical understanding of dependence by solving examples/problems.

• Most of statistics is the study of how one variable depends upon another. There are many tools that assume IID, but the vary in their sensitivity to dependence violation. So, some tools are better than others when it comes to dealing with this situation. My understanding is that many non-parametric methods tend to be less sensitive to such assumptions, for example. However, I am not very experienced in non-parametric statistics. So, the real question is what test is right, given your problem? – John Yetter Dec 2 '15 at 16:47
• "Independence" is, in some sense, conceptually singular, whereas non-independent could be anything else. Thus there won't be a unified treatment of non-independent data, but there will be methods for different situations. Prototypical analyses for non-independent data would be various flavors of mixed-models or time-series models, but those in no way exhaust the possibilities of non-independent data. You will need to specify exactly what kind of non-independence you are interested in. – gung - Reinstate Monica Dec 2 '15 at 16:57

• @Andrey start with the site search facilities. A search for [references] [copula] will locate this for example, a search for [references] [time-series] would find this, among others, and so on (also if it's not already your default, once you search, click to sort the result by votes). – Glen_b -Reinstate Monica Dec 3 '15 at 22:49