Autarchy of the Private Cave

Original PDF.
My local copy.

Usually I’m using 10-fold (non-stratified) CV to measure the predictive power of the models: it gives consistent results, and is easy to perform (at least on smaller datasets).

Just came across the Akaike’s Infor­ma­tion Criterion (AIC) and Schwarz Bayesian Infor­ma­tion Criterion (BIC). Citing robjhyndman,

Asymp­tot­i­cally, min­i­miz­ing the AIC is equiv­a­lent to min­i­miz­ing the CV value. This is true for any model (Stone 1977), not just lin­ear mod­els. It is this prop­erty that makes the AIC so use­ful in model selec­tion when the pur­pose is prediction.
…
Because of the heav­ier penalty, the model cho­sen by BIC is either the same as that cho­sen by AIC, or one with fewer terms. Asymp­tot­i­cally, for lin­ear mod­els min­i­miz­ing BIC is equiv­a­lent to leave–v–out cross-​​validation when v = n[1-1/(log(n)-1)] (Shao 1997).

Want to try AIC and maybe BIC on my models. Conveniently, both functions exist in R.

• R time series tutorial (2010, a website of the “Time Series Analysis and Its Applications: With R Examples” book)
• Statistics with R (2007)
• R for programmers PDF (2008, 104 pages, linked to from here)
• Brief R tutorial (2004)
• Statistical computing with R: a tutorial (2004)
• An introduction to R (from the official r-project website, should be always up-to-date)
• R tutorial (date unknown, definitely newer than 2005)

MathIsFun offers nicely illustrated pages on math, algebra, geometry and maybe more.

For example, there is a step-by-step instruction on calculating variance and standard deviation for a set of measured dog heights, with a final picture (below) illustrating one-sigma distance from the mean. Unfortunately, concepts of normal distribution and %% of data points within each sigma range are not discussed, but that might as well be too much for a nice explanation. There are also animations, like this mean machine. Overall, MathIsFun is a nice resource for younglings.

I am doing some simple statistics now, and had to review some basic concepts like standard deviation.
As a note to myself and anyone interested, here it stays.

The mean is just a sum of all your numerical observations, divided by the number of observations. E.g., if you have measured how tall your 5 children are, and got the values 1.42, 1.56, 1.05, 1.89, 1.92, the “mean height” of your children will be x = (1.42 + 1.56 + 1.05 + 1.89 + 1.92) / 5, x = 7.84 / 5 = 1.568 (all values in metres).

The mean itself doesn’t tell you much, however. If you had this 1.568 mean available, you wouldn’t know even the range of heights.

The standard deviation helps with this. First of all, it is measured in the same units as initial data – i.e. metres in our example. Second, it gives you an idea of how strongly do the measured values differ in your sample – the bigger the deviation, the longer is the value range measured in the sample.
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