Computer simulations of photon transport through an absorbing and/or scattering medium form an important research tool in astrophysics .
Nearly all software codes performing such simulations for three-dimensional geometries employ the Monte Carlo radiative transfer method , including various forms of biasing to accelerate the calculations .
Because of the probabilistic nature of the Monte Carlo technique , the outputs are inherently noisy , but it is often assumed that the average values provide the physically correct result .
We show that this assumption is not always justified .
Specifically , we study the intensity of radiation penetrating an infinite , uniform slab of material that absorbs and scatters the radiation with equal probability .
The basic Monte Carlo radiative transfer method , without any biasing mechanisms , starts to break down for transverse optical depths \tau \gtrsim 20 because so few of the simulated photon packets reach the other side of the slab .
When including biasing techniques such as absorption/scattering splitting and path length stretching , the simulated photon packets do reach the other side of the slab but the biased weights do not necessarily add up to the correct solution .
While the noise levels seem to be acceptable , the average values sometimes severely underestimate the correct solution .
Detecting these anomalies requires the judicious application of statistical tests , similar to those used in the field of nuclear particle transport , possibly in combination with convergence tests employing consecutively larger numbers of photon packets .
In any case , for transverse optical depths \tau \gtrsim 75 the Monte Carlo methods used in our study fail to solve the one-dimensional slab problem , implying the need for approximations such as a modified random walk .