Cyan comments on Thinking like a Scientist - Less Wrong
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Comments (25)
I was struggling to word the doctor parapgraph in a manner which was succinct but still got the idea across. I think query worded it better.
On math curriculum, that advanced classes build off of calculus is a function of current design. They could recenter courses around statistics and have calculus be an extension of it. Some of the calculus course would need to be reincorporated into the stats courses, but a lot of it wouldn't. You're going to have a hard time convincing me that trigonometry a̶n̶d̶ ̶v̶e̶c̶t̶o̶r̶s̶ are a necessary precursor for regression analysis or Bayes' theorem. The minority of students in physics and engineering that need both calculus and statistics should not dictate how other majors are taught. Fixing the curriculum isn't an easy problem, but they've had more than a century to solve it and there seems to be little movement in this direction.
So you're fitting a straight line. Parameter estimates don't require linear algebra (that is, vectors and matrices). Super. But the immediate next step in any worthwhile analysis of data is calculating a confidence set (or credible set, if you're a Bayesian) for the parameter estimates; good luck teaching that if your students don't know basic linear algebra. In fact, all of regression analysis, from the most basic least squares estimator through multilevel/hierarchical regression models up to the most advanced sparse "p >> n" method, is built on top of linear algebra.
(Why do I have such strong opinions on the subject? I'm a Bayesian statistician by trade; this is how I make my living.)