unbiased estimation of a reciprocal

As often, I came a’X this 2007 paper following an X-validated (if poorly worded) question that linked to it. With weird arguments:

Computing an unbiased estimate of the integral induced by an unnormalised density f is a poor sales argument, as the renormalised object is not a probability density. Call to the unbiased approximation of Bayes factors the paper does not!
The proposed solution involves a replacement of the unnormalised density f by a substitute and normalised density h that leads to the identity

$\frac{f(y)}{\int f(x)\text dx}=\frac{hf(y)}{1-\int [h(x)-h(y)f(x)/f(x)]\text dx}=\frac{hf(y)}{1-a(y)}$

with the assumption that the function a is between -1 and 1, which requires some insight about the connection between f and h.

The unbiased estimator is an infinite power series in a(y). Requiring an increasing number of independent generations as the power grows.
The series is unbiasedly terminated by playing roulette (if not Russian roulette!). Stopping when the k-th power estimate is below a certain bound. To be selected with no preliminary knowledge of the range of a.
The uncertainty attached to the power series estimate is not evaluate and could reach the concerning level of an infinite variance.

that may explain for its limited popularity.

Xi'an's Og