I am trying to fit a model of the form: for(i in 1:N) X[i] ~ multinomial(theta); theta ~ dirichlet(exp(alpha)); alpha ~ normal(0,1); where alpha is a univariate parameter. Unsurprisingly, this model – being non-centred – suffers from divergent iterations. These do not go away if I increase adap…

I think you want to integrate out theta in this situation, i.e. use a multinomial-Dirichlet likelihood for the data. Dirichlet-multinomial distribution | Dirichlet-multinomial as a compound distribution The Dirichlet distribution is a conjugate distribution to the multinomial distributi…

Thanks Ben, I hadn’t thought of that. It looks like Bob’s done the hard work for me of coding up the log probability: https://groups.google.com/forum/m/#!topic/stan-users/uhrIEddZ2I8

In case it’s helpful, I’ve just had to implement Bob’s solution, so this is what your functions block would probably look like if you implemented a probability mass function for the Dirichlet-Multinomial: functions { real dirichlet_multinomial_lpmf(int[] y, vector alpha) { real alpha_plus = s…

Thanks for posting. This is about as efficiently as it can be implemented without custom derivatives in C++. You don’t need parens around return values. And it’s conventional to start new lines with operators rather than end them that way (easier to scan) in languages that allow it (R doesn’t as …

Thanks Bob, I’ve implemented your style suggestions.

I was thinking about the RNG function of this dirichlet_multinomial_lpmf I found this issue on github. [image] Issue: Dirichlet-multinomial density and (P)RNGs opened by syclik on 2015-07-06 From @bob-carpenter on November 11, 2014 16:31 density dirichlet_multinomial_lo…

Yes, that’ll work for the RNG. I’d just write that as: int[] dirichlet_multinomial_rng(vector alpha, int N) { return multinomial_rng(dirichlet_rng(alpha), N); } You could also test that each alpha[k] > 0 and is finite, and that N >= 0.

In using y[n] ~ dirichlet_multinomial( precision * softmax( X[n] * beta ) ) with a large array (~ 1K-20K), I get the vector softmax(X[n] * beta ) that includes incredibly low values. If I want to achieve unimodality in the dirichlet part I need all parameters to be > 1. I am attempting to set par…

Check out this thread - it’s on sum to zero constraints, but may be relevant for the sum to 1 constraint. [image] Test: Soft vs Hard sum-to-zero constrain + choosing the right prior for soft constrain Modeling I think the first question is why the soft constraint gets such…

What should the posterior look like? Should it be a lot of effectively zero values? Or should it be smoothed to look more uniform? That scaling is introducing a non-identifiability. It’d be better to declare: parameters { real<lower = 0> precision_delta; ... model { matrix[? , ?] X_beta = X…

Non-centred parameterisation for Dirichlet distribution

Modeling

aaronjg June 14, 2018, 2:41am 10

Check out this thread - it’s on sum to zero constraints, but may be relevant for the sum to 1 constraint.

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Non-centred parameterisation for Dirichlet distribution

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