Any methods for predicting outliers? I understand that most statistical methods focus on predicting common occurrences, but are there any tests that would predict outliers? Essentially I would want to know what outside variables stand out for outliers as opposed to "normal" values. An improvised example being predicting a stellar performance on a game (10+ points) rather than 0-9.9 points. I would then want to figure out which physical traits (out of lets say, 200) are abnormal for individuals with a stellar score rather than anything less.
I've gotten some significant results that lower AIC using logistic regression (1 = outlier, 0 = not), but I'm not completely sure if it will hold up in the long run or if it is even appropriate to recode the continuous variables into binary ones.
 A: Parametric statistical tests make assumptions about the distributions of the variables involved (nonparametric tests make assumptions about the distributions of ranks of the data). These distributions describe the probability not only of "common occurrences" but of rare ones. If by "outlier" you mean "uncommon occurrence," then the answer to your question is "yes."
If by "outlier" you specifically mean unlikely values in a predictor variable such as the $x$ in $y = \beta_{0} + \beta_{x}x + \varepsilon$; where $\varepsilon \sim \mathcal{N}\left(0,\sigma_{y|x}\right)$, then not really: the aim of such a model is to explain or predict $y$, not $x$. However, there are techniques (e.g., Cook's D, etc.) for examining the sensitivity of such models to the influence of outliers.
A: Quantile regression can predict various quantiles.  If you choose a high (or low) quantile, that might get at what you want.  It depends on how "out" the outlier is.
Tree methods could also work, with appropriate options. 
