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No, the "true model" he seems to be referring to is the mean of the distribution of the noisy observations. In the example, the distribution is the normal distr
by unfamiliar 10y ago
No, the "true model" he seems to be referring to is the mean of the distribution of the noisy observations. In the example, the distribution is the normal distribution and the mean is log(x), which he is referring to as the "true model".
The notation is pretty sloppy for someone handing out statistical advice.
- nabla9 10y agoI don't think his usage of these terms is sloppy at all. The main point of his argument is that R² compares to observed mean and not into true model behind the data. Terms "true model", "true distribution" and "true population" are well defined concepts in statistics – unless Jorma Rissanen is nearby.
- bunderbunder 10y agoThe true model is y = log(x) + u Where u is an error/noise term, and in this case takes a normal distribution. The error term is meant to Hoover up all the stuff you can't account for because it's impossible to measure everything. As ever, what you're trying to estimate is the parameters for everything but the error term. He's maybe being a little sloppy with the notation, but TBH it's a pedantic distinction that I haven't seen anyone make a big deal of since I last took intro stats. In R, for example, you'd specify the model as "y ~ log(x)" and leave it at that.