Please see my edit for a more concise description of my question
Ever since I started looking into the mathematics behind path-tracing algorithms, there has been one question that I haven't been able to find an answer to: How are deterministic samples weighted in an importance sampled Monte Carlo estimation? By deterministic samples, I mean values that will ALWAYS be sampled, as opposed to values which are sampled probabilistically. In importance sampling, non-uniform sampling can be achieved without introducing any bias, by dividing the value of a sample by it's probability of being chosen from a given distribution function. Deterministic samples can't be represented in a probability distribution function, since they are inherently non-probabilistic.
My question is: if a specific value or range of values are always sampled, how are they weighted in order to not introduce statistical bias?
This is a core mathematical principal behind path-tracing, as samples which connect vertices of a path, which is probabilistically drawn, to light sources are always sampled, in order to reduce variance. This is somehow done without introducing statistical bias, yet I cannot find any information on how this is achieved.
EDIT: I have done some more research, and gotten closer to the answer, yet some question still remain.
After reading this paper on Multiple Importance Sampling, I have discovered the combined sample density function:
here "n" represents the number of sampling strategies used, "
" the fraction of samples taken with strategy k, and "
" being the probability distribution function of strategy k.
MY REMAINING QUESTION IS: What would be the probability density function () for a sampling strategy which only samples a single value? It can't be infinite, otherwise path-tracing algorithms could not handle point, or purely directional light sources, as directly sampling them would contribute an infinitely small amount towards the final estimation of radiance.