Is there any statistical analysis of the security of a "Brain Wallet"?
There are roughly 170,000 words in the english dictionary according to this link. If you combine 4 random words (170,000^4) , you get 8.3*10^20 potential combinations which is more than 2^64 (1.8*10^19). However 64 bits of security is generally considered weak these days.  Bitcoin uses 256 bit keys (1.1*10^77 combinations) so if you want that level of security you need to use at least 15 words (2.8*10^78). Altering cases will obviously increase the potential combinations by a significant factor. Different languages have different number of words so that will change the calculations as well. 

This calculation only applies if you choose the words completely randomly. People keep ignoring this important detail, and is the reason why brain wallets are not recommended. There are many cases of people getting their bitcoin cleaned out because they choose common phrases or include commonly used words in their private key.