Estimating Basal Eurasian ancestry?

Basal Eurasians (BE) are a hypothetical ghost population that apparently split from other Eurasians no later than 45,000 years ago. If they actually existed, they had a significant impact on the ancestry of early Neolithic farmers, and thus all present-day West Eurasians.

Testing ancestry proportions from ghost populations isn't easy. However, Haak et al. 2015 made use of an f4 equation that seemingly gave an accurate estimate of BE admixture in LBK farmer Stuttgart: f4(Stuttgart,Loschbour;Onge,MA1)/f4(Mbuti,MA1;Onge,Loschbour) = 44%. The other LBK farmers scored an average of 40% BE, which also made sense.

Unfortunately, this equation doesn't appear to work too well for Caucasus Hunter-Gatherers (CHG) Kotias and Satsurblia. They both score around 25% BE, which, as far as I can see, seems way too low. Perhaps using MA1 in the equation is messing things up because CHG harbor significant MA1-related ancestry?

I tinkered around with Haak's equation and came up with this: f4(X,Iberia_Mesolithic;Dai,Karelia_HG)/f4(Mbuti,Karelia_HG;Dai,Iberia_Mesolithic). The results look solid, at least in relative terms (see image below). But is the equation actually valid?

My main worry is using both Iberia Mesolithic and Karelia HG. They share a lot of drift, much more than Loschbour and MA1. Also, even though both Dai and Onge belong to the so called Eastern non-African (ENA) clade, they're quite distinct, with Dai a lot less basal in the context of ENA diversity. Any thoughts? Suggestions?

Update 04/18/2016: Interestingly, my f4 equation essentially fails for most post-Neolithic Europeans, particularly those with relatively high ratios of Karelia HG-related ancestry. For instance, Yamnaya Kalmykia scores just 2.9% BE, which can't be right. Yamnaya Samara shows -2.2%, which is obviously wrong.

But I tried several combinations of reference samples and found that by replacing Karelia HG with Hungary HG and Dai with Ust-Ishim I was able to obtain coherent results for a wider range of groups, including Yamnaya.

To be honest, I still don't know what the hell I'm testing here exactly. The results appear to reflect the existence of two components within West Eurasia; one representing ancient hunter-gatherers from Europe and probably surrounding areas of the Near East, and another closely related to present-day Near Eastern populations. The latter might well be a signal of the so called Basal Eurasians, or perhaps a number of as yet unsampled meta populations from the ancient Near East?