Why isn't RANSAC most widely used in statistics? Coming from the field of computer vision, I've often used the RANSAC (Random Sample Consensus) method for fitting models to data with lots of outliers. 
However, I've never seen it used by statisticians, and I've always been under the impression that it wasn't considered a "statistically-sound" method. Why is that so? It is random in nature, which makes it harder to analyze, but so are bootstrapping methods. 
Or is simply a case of academic silos not talking to one another?
 A: For us, it is just one example of a robust regression -- I believe it is used by statisticians also, but maybe not so wide because it has some better known alternatives.
A: I think that the key here is the discarding of a large portion of the data in RANSAC. 
In most statistical applications, some distributions may have heavy tails, and therefore small sample numbers may skew statistical estimation. Robust estimators solve this by weighing the data differently. RANSAC on the other hand makes no attempt to accommodate the outliers, it's built for cases where the data points genuinely don't belong, not just distributed non-normaly.
A: This sounds a lot like bagging which is a frequently used technique.
A: You throw away data with RANSAC, potentially without justifying it, but based on increasing the fit of the model. Throwing away data for increased fit is usually shun as you may loose important data. Removal of outliers without justification is always problematic. 
It is ofcourse possible to justify it. E.g. if you known the data should follow a given pattern, but that there also are deviation in the data from the pattern due to error in the measurements. 
