Simplify the distribution of the sum of multiple logistic responses

[Bob_Carpenter]

I posted the dynamic programming algorithm for the Poisson binomial here:

Poisson-binomial distribution - any existing Stan implementation?

Here’s a more efficient Stan version that works on the log scale for arithmetic stability is quadratic in the size of the vector of probabilities avoids doing (most) unnecessary calculations only returns a single value It could be easily modified to produce an efficient lcdf or lccdf. functions { /** * Return the Poisson-binomial log probability mass for the specified * count y and vector of probabilities theta. The result is the log * probability of y successes in N…

There might be some mileage for dropping in that theta has a log odds structure. We have a log_inv_logit function and log1m_inv_logit built in.

If people really use this, we could code it as a built-in for Stan.