In implementing a dirichlet_multinomial model (with 1K - 20K categories) model{ ... y[n] ~ dirichlet_multinomial( precision * softmax( X[n] * beta ) ) } I have noticed that there is not a single value for precision that fits well all the data. That is, the abundant categories have much varia…

Analogously to what dirichlet-multinomial is (I am using the conjugate more efficient implementation, the following implementation is just for discussion) dirichlet-multinomial paramters { simplex[K] theta[N]; // addition of many intermediate parameters matrix[K, R] beta; real<lower=0> xi;…

I don’t really follow what are the mechanisms/features of your data that you are trying to model with either the Dirichlet-multinomial, Negative-bionimial-softmax-multinomial or Gamma-multinomial models. I think it would be hard to make progress without sorting this out. In particular, I remain unco…

[image] martinmodrak: So negative binomial seems to be a good model for mRNA counts in cells (before we sequence). Yes I agree this is probably the best simple model on what is going on at the tissue/cell level. [image] martinmodrak: IMHO the multinomial model is appropriate for step 7 a…

[image] stemangiola: however the multinomial will still model the uncertainty of tubes that have been sequenced deeply (more extraction) versus tubes that have little number of reads (carry less information, and the data have less weight). But this can also be modelled in the neg. binom. fram…

[image] martinmodrak: Why would that be inappropriate in your case? It might model indirectly the same two NB → multinomial generative process. I would like to involve @Bob_Carpenter in this conversation as he can have a better idea.

[image] martinmodrak: IMHO the multinomial model is appropriate for step 7 at best, but then it would need to be multinomial model over neg. binom initial counts. I don’t follow this. We take a finite sample and then keep chopping it up. Never do we have an open-ended count distribution lik…

This is actually a quote from @martinmodrak : [image] stemangiola: would however guess that the negative correlations induced by multinomial (e.g. that sequencing a lot of a single gene means less copies of other genes are sequenced) is negligible, since the proportion of each gene among the tot…

[image] Bob_Carpenter: What’s a lane When you sequence, some samples/tubes can be put in external lanes of the sequencing chip, and this can affect sequencing thus be a confounding factor (I guess this technical artefact depends on the technology used). This however depends on the sequencing …

I think you are overestimating the amount of order to be found in biology :-) But I’ll be happy to be proven wrong. Please keep in mind though that what follows is a computer scientists’s understanding of complex biology, so there is grain of salt to be taken. The claim I was trying to make is that…

[image] martinmodrak: the marginal distribution of mRNA counts for most genes across replicates will be overdispersed Poisson. I’m sure that’s just an approximation, too. My point was just that when you look at your steps 1–3, they’re giving you a mechanism with which to model the overdisper…

More flexible than Dirichlet-multinomial: gamma-multinomial (?)

Modeling

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More flexible than Dirichlet-multinomial: gamma-multinomial (?)

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