Editing Quasi-Monte Carlo method (section)

== Drawbacks of quasi-Monte Carlo ==
Lemieux mentioned the drawbacks of quasi-Monte Carlo:<ref name="lemieuxbook">Christiane Lemieux, ''Monte Carlo and Quasi-Monte Carlo Sampling'', Springer, 2009, {{ISBN|978-1441926760}}</ref>
* In order for <math> O\left(\frac{(\log N)^s}{N}\right) </math> to be smaller than <math> O\left(\frac{1}{\sqrt{N}}\right) </math>, <math>s</math> needs to be small and <math>N</math> needs to be large (e.g. <math> N>2^s </math>). For large ''s'', depending on the value of ''N'', the discrepancy of a point set from a low-discrepancy generator might be not smaller than for a random set.
* For many functions arising in practice, <math> V(f) = \infty </math> (e.g. if Gaussian variables are used).
* We only know an upper bound on the error (i.e., ''ε'' ≤ ''V''(''f'') ''D''<sub>''N''</sub>) and it is difficult to compute <math> D_N^* </math> and <math> V(f) </math>.
In order to overcome some of these difficulties, we can use a randomized quasi-Monte Carlo method.