Just because alternative methods aren't widespread, it doesn't necessarily mean they are "more complicated", just that rely on different assumptions. I'm reall

Just because alternative methods aren't widespread, it doesn't necessarily mean they are "more complicated", just that rely on different assumptions. I'm really excited, for example, about "model-free" time series methods emerging from non-linear topological data analysis. Takens' embedding theorem shows that low dimensional "shadows" of high dimensional attractors can be constructed from a time series alone, and that they can reveal deep, useful facts about system a time series is part of, even if that system defies geometric modeling. These kinds of methods are radically different from conventional statistical methods. see here: https://www.youtube.com/watch?v=NrFdIz-D2yM https://www.youtube.com/watch?v=NrFdIz-D2yM Previously, researchers found themselves flailing around with geometry, trying to come up with models that accurately described the dynamical nature of the systems they were studying (e.g. fish populations). A model might work well for a few years, then stop working. These topological methods cut through and get straight to the underlying relationships that drive various observables in a complex system, without relying on fickle geometric assumptions about how exactly those relationships will be expressed.