Estimation of capture rate and moi with generative model

[Andrew]

Reading through the supplemental methods of Dixit et al. and there is a generative model described for MOI and capture rate estimation. I understand the premise of the model, but do not understand what the value "m" is in the equation as it is not described in the text. It seems that the purpose of the equation is to incorporate information about the possibility that a cell observed to have K guides actually originated from a cell carrying j guides (a higher number of guides) due to incomplete detection. Given this, the way the binomial term in the equation is written is confusing to me as you are asking about j successful detections, when I would have expected the question to be centered around k successes in j trials. Would you be able to verify that the equation in the supplement is correct and if so, clarify the m parameter, etc?

Thanks very much for the help!

Andrew

[Atray Dixit]

Hi Andrew,

My apologies. Your expectation is absolutely correct; nice catch! The equation should be revised as follows:

I've also posted code with an example here.

Let me know if you have any more questions.

Thank you for bringing this up!

Atray

[Andrew]

Thanks very much for the clarification, that makes much more sense to me now and the ipython notebook was also very helpful, thanks for posting!

[oana...@gmail.com]

I have a quick question. 

Should the equation above be 

sum(k=0 to 10) [ O(k) log ...] 

rather than 

sum(k=0 to 10) [ log (O(k) ...)]

I thought the O(k) comes from multiplying the convolved distribution O(k) times (as each cell would be an independent event like this). So then when you take the log it becomes a sum. The code indeed is consistent with sum(k=0 to 10) [ O(k) log ...], if I understand correctly:

        for k in range(len(n)):

            ll+=n[k]*np.log(zibpdf[k])

        LL[i,m]=ll

Or am I not understanding this correctly?

Thanks!

[Atray Dixit]

Nice catch, and I believe that is correct!

Looks like there were a couple of typos in the equation in the paper.