Does film filter introduce bias in path tracing? Does using box or gaussian filter introduce bias to the image when reconstructing the pixel?
Bias does not seem to be talked in the Chapter 7.8 of PBRT
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.