Fast implementation of reverse unfinished beta function in C ++

Question

I am looking for an implementation of an inverse incomplete beta function, possibly already written in C ++ or simple to implement. However, I need it to be FAST! As in, I will run this in the optimizer's inner loop, so it will hopefully take a couple of hundred clock cycles.

There are already several threads here, but in this case, I am ready to drop the greater accuracy for speed. In addition, the domain is somewhat limited, since I only use integer values ​​for a and b.

More information about the problem: I give an integer number of trials n and an integer k <= n of these trials that were successful. I assume that the background distribution for the base probability of a successful test is uniform in [0,1], so given that I have seen a number of trials and successes, my subsequent distribution should be a beta distribution. In the Bayesian model, I essentially try to find the pth percentile of probable underlying probabilities.

Again, I do not need it to be very accurate, just fast. I can cope with an error of up to +/- 1%. However, this cannot be extremely inaccurate for small numbers: my inputs range from almost zero to tens of thousands.

Thanks in advance! If any clarification is necessary, let me know.

Answer 1

• One approach is to create a table. If you need to distinguish, you will need to interpolate it. This is probably the only alternative for you, if you keep everything except one of the options fixed, but I think you are doing this? (OP says no)

  You might want to make the binning table non-linear to get good accuracy at low x values, as you requested. Try a hopper size proportional to x, x ^ 2, etc.

• Use a simple search method like http://en.wikipedia.org/wiki/Secant_method to find your value as a function of expanding the power (not the reverse) of an incomplete beta function. http://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function . This only works if it is monotonous.

• First, make sure you really need your own method. Perhaps try them first? http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html