Obstructions to Sampling Qualitative Properties

Background

Sampling methods have proven to be a very efficient and intuitive method to understand properties of complicated spaces that cannot easily be computed using deterministic methods. Therefore, sampling methods became a popular tool in the applied sciences.

Results

Here, we show that sampling methods are not an appropriate tool to analyze qualitative properties of complicated spaces unless RP = NP. We illustrate these results on the example of the thermodynamically feasible flux space of genome-scale metabolic networks and show that with artificial centering hit and run (ACHR) not all reactions that can have variable flux rates are sampled with variables flux rates. In particular a uniform sample of the flux space would not sample the flux variabilities completely.

Conclusion

We conclude that unless theoretical convergence results exist, qualitative results obtained from sampling methods should be considered with caution and if possible double checked using a deterministic method.