Incomplete beta function causing hypergeometric gradient error

Modeling
1

I have a normalising factor for a probability distribution that requires me to evaluate an incomplete beta function. When I run the model I get the error “grad_2F1: k (internal counter) exceeded 100000 iterations, hypergeometric function gradient did not converge”. Is this a well-known error? The bounds on the parameters are 0<R<\inf, 2<K<10.

functions {
    real log_funcF0(real VIN, real VOUT, real K){
        real R = VOUT/VIN;
        return -log(VIN)+log(inc_beta(1.0/K,1.0-1.0/K,R^K/(1.0+R^K)))-log(K*R);
    }
}
2

I managed to get round this bug with some mathematical trickery. You can re-write the incomplete beta using this identity and then you don’t get the non-convergence error messages in this area of parameter space.

inc_beta(a,b,x) = beta(a,b)-inc_beta(b,a,1-x)

Edited: I had to edit the identity to use Stan’s definition of the incomplete beta function.

3

this is something we can do internally. It would help if you could print out some parameter values ( parameters you call inc__beta with) in your program that cause the error.

4

Here are a couple examples, where R and K refer to the parameterisation above.

R = 10.4216, K = 4.97921
R = 12.2444, K = 6.14438

I can generate more examples if needed!

1 Like
5

This is likely good enough since the rest of the calculation is deterministic. The underlying functions are calculated by a few different algorithms depending on the part of parameter space and it’s helpful to have a starting point