Does film filter introduce bias in path tracing?
This is an answer to your comment rather than the title of your question. It can be considered as a partial answer.
The bias in path tracers are introduced by the estimators.
For example, think of the following two equations:
$$ I = \int_{\Omega} f(\omega) d\omega $$
$$ F = \frac{1}{N} \sum_{i}^{N} \frac{f(\omega)}{p(\omega)}$$ where $p: \Omega \to R$.
It should be evident that as the number of samples N increases, the function $F$, ie the estimator, outputs values that are closer to $I$.
The unbiased estimator satisfies the following $E[F_N] \approx I$ or $\lim_{N\to\infty}F_N=I$, that is the expected value of the estimator matches the desired outcome in $I$ as the number of samples goes to infinity.
The biased estimator does not offer such a guarantee.
You can read more from D. Van Antwerpen's master thesis, I am giving the full citation in case the link goes away:
Van Antwerpen, Dietger. “Unbiased Physically Based Rendering on the GPU.” Master of Science in Computer Science, Delft University of Technology, 2010.