I was getting into GWAS methods for estimating heritability, and it turns out there are two major statistical practices used for this, GCTA and LDSC . The older one is GCTA, so naturally I started reading about it first. This set me down a rabbit hole of confusion. Whereas LDSC and everything else I’ve seen uses standard OLS , GCTA does not. GCTA uses “BLUP.” Why not just normal OLS? To understand this, we have to understand what BLUP is. What is BLUP? BLUP is an acronym that stands for “Best Linear Unbiased Predictor.” Spoiler! It’s neither best nor unbiased. While it is a linear model, estimating it will rip you from the realm of linear algebra into nonlinear optimization metho
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