Seeing language from the DNA

[Jaska]

Just to get some perspective. Where and when do you consider it possible (let's say with >1% probability) (by whatever standard of evidence you like) that for, let's take the most common and familiar subject of debate, PIE (take that loosely so as not to get sidetracked on the nitty gritty of what that constitutes) was spoken?

Here it is presently important to distinguish two stages: 
1. Early Proto-Indo-European = Proto-Indo-Anatolian.
2. Late Proto-Indo-European = all the rest, or sometimes without Tocharian.

To my knowledge, the best arguments still support the steppe homeland for LPIE. All the relevant arguments have been recently considered in Anthony & Ringe 2015:
https://www.academia.edu/10597023/Anthon...l_evidence

It has been possible to derive even the Anatolian branch from the steppe. Recently some geneticists have proposed the Caucasus Region, which could be correct, if language should always follow the majority ancestry component. But we know that this is not the case in our reality.

More important would be the linguistic evidence, but at that time depth and in this situation we still do not have undisputed winner based on paleolinguistic evidence. Results concerning distant relatedness or ancient contacts are contradicting: PrePIE could have been spoken in the northeast, close to Pre-Proto-Uralic; or it could have been spoken in the south, close to the Caucasian language families. So ancient times are probably forever beyond the reach of reliable linguistic methods, so it is possible that we will never get the answer. It means that all possibilities must be kept open.