Hi, I am very new to Stan, and I would really appreciate some guidance and advice on modelling a problem. I have count data from three underlying sources. I assume each source can be modelled as a negative binomial distribution NB(r, p), where r is the number of failures until the experiment is sto…

Since you have measurements that correspond to different parts of the sum, then you might be able to estimate p1, p2, and p3 separately. Otherwise assuming the r/p → mu/phi transformations are alright, then this seems fine. Is the goal of the gamma(0.01, 0.01) priors to make a spike near zero? I w…

Thanks for responding. As I see it, the other problem with estimating p_1, p_2, and p_3 individually, is that getting the individual r_i and p_i is also going to be complicated because y_Y and y_Z are sums of NB distributions. And what I really am after is getting the individual parameters. As far a…

[image] larryns: does not have a nice closed-form solution Oooh yeah good point. I don’t know of a way around that. I don’t have any other suggestions off hand. If you’re able to generate data from your model and fit it back and that looks vaguely good, that’s a super solid step 1. You migh…

Thanks so much for the advice and feedback. Everything seems to be working fine, so I guess so far so good. I’ll have a look at the article you sent too, thanks again!

[image] bbbales2: Oooh yeah good point. I don’t know of a way around that. Check this out. @martinmodrak can give more details.

Thanks @maxbiostat . I’ll look through the blog by @martinmodrak . I have very limited experience with saddlepoint approximations though and my impression was that they’re not very good and don’t have full support. I’ve seen some implementations where they try to improve the approximations by adopting…

[image] larryns: Thanks @maxbiostat . I’ll look through the blog by @martinmodrak . I have very limited experience with saddlepoint approximations though and my impression was that they’re not very good and don’t have full support. I’ve seen some implementations where they try to improve the appro…

First, a big thank you to @martinmodrak for your insight. I read your blogpost and tried to follow your lead for my model. Here’s the code for reference, and hopefully it’ll help anyone else working on a similar problem: functions { /* Using the method of moments approximations for computing mu a…

[image] larryns: My assumption is that the mean of yXy_X should be small, yYy_Y moderate, and yZy_Z highest. Hence, the gamma priors I chose. I don’t think those priors do this. gamma(0.01, 0.01) has mean 1 while gamma(5, 10) has mean 0.5, and only 1% prior probability for values > 1.16. Thos…

@martinmodrak thank you again, especially for taking the time to run the code and simulate data, etc. I had concerns about the priors, and you confirmed my thoughts. It turns out that I assumed the wrong parameterization for gamma, and I should have double-checked, so thanks for pointing out that pr…

Parameter estimation for the sum of negative binomial distributions

Modeling

maxbiostat February 28, 2021, 8:41pm 6

Check this out. @martinmodrak can give more details.

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Parameter estimation for the sum of negative binomial distributions

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