How to integrate sample likelihoods from different replicates

[nickhir]

We performed a perturbation experiment with 2 replicates (2 WTs and 2 KOs). When I concatenate the datasets and plot them on a UMAP it is very obvious that there is minimal overlap between the 2 replicates:

Since it is not advisable to do batch correction when running MELD (#50) I decided to analyze the replicates separately (i.e. WT1 vs KO1 and WT2 vs KO2) to get sample densities and likelihoods for both replicates individually.

In this issue (#56), @dburkhardt mentioned to "compare the magnitude of MELD likelihoods as if they were calculated on the same graph". I was wondering if you could elaborate what you mean by this. Because we dont have any cells that are shared between replicate 1 and replicate 2, how should we compare the likelihoods, calculate the mean likelihood or estimate standard derivations?

Any help is much appreciated!