What is the benefit of OU vs regression for modeling data, say data in the form of (x,y) pairs?

ajumbaretu 2022-11-20 Answered
What is the benefit of OU vs regression for modeling data, say data in the form of ( x , y) pairs?
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reinmelk3iu
Answered 2022-11-21 Author has 21 answers
Stochastic processes and regression analysis are just two sides of the same coin. Namely, Assume that you have a realization from a univariate time process and you postulate that the process that generated this data was autoregression of order 1, however with an unknown coefficient ϕ. I.e., X t = ϕ X t 1 + ϵ t , hence you can use statistics (regression analysis) in order to estimate ϕ. Now, assume that you are not sure what process generated your data and you are willing to test a set of AR(I)MA models. Here too the statistics might help you to select the most appropriate model. Namely, parametric-regression models allow you to approximate the data-generating process by a linear regression. Note that not every stochastic process can be well approximated by a linear-parametric regression model. And, basically, stochastic analysis assume that you know the properties of the process and you can work with them, while regression analysis assume that you don't know the data-generating process and you try to recover its properties by using the data.
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i'm seeking out thoughts for a 15-hour mathematical enrichment course in a chinese language high faculty. What (pretty) simple concern would you advocate as a subject for any such course?
historical past/issues:
My students are generally pretty good at math, but many of them have no longer been uncovered to rigorous or summary mathematical reasoning. an amazing topic would be one that could not be impossibly hard for students who have by no means written or study proofs in English.
i have taught this magnificence three times earlier than. (a part of the purpose that i'm posting that is that i have used up all my thoughts!) the primary semester I taught an introductory range theory elegance (which meandered its way toward a proof of quadratic reciprocity, though I think this become in the end too advanced/abstract for some of the students). the second one semester I taught fundamental graph idea and packages (with a focal point on planarity and coloring). The 1/3 semester I taught a class at the Rubik's dice.
the students' math backgrounds are pretty numerous: a number of them take part in contest math competitions, and so are familiar with IMO-fashion techniques, however many aren't. a number of them may additionally realize some calculus, however I cannot assume it. all of them are superb at what in the united states is on occasion termed "pre-calculus": trigonometry, conic sections, systems of linear equations (though, shockingly, no matrices), and the like. They realize what a binomial coefficient is.
So, any ideas? preferably, i'd like to find some thing a bit "sexy" (like the Rubik's cube) -- tries to encourage wide variety theory through cryptography seemed to fall on deaf ears, however being capable of "see" institution idea on the cube became pretty popular.
(Responses specifically welcome from folks who grew up in the percent -- any mathematical subjects you desire were protected within the excessive college curriculum?)