Practice question · Multiple choice
Monte Carlo error falls like 1/√N. To gain one more decimal digit of accuracy, what does that cost?
Hints
- Error ∝ 1/√N. Solve for the N that divides the error by 10.
- Ask what √N must do for 1/√N to fall by a factor of ten.
Show the answer
B. A hundredfold increase in samples, since error falls like 1/√N
Why
√N must grow tenfold, so N grows a hundredfold, brutal for high precision. It is tolerated because the rate is independent of dimension, so in 300 dimensions where grid methods are impossible it is the only option, and three or four digits is usually all anyone needs.
Practise Vectorised Computation and Libraries
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