A Monte Carlo simulation of the density of a glass marble
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Data analysis and model fitting in the laboratory
Measurement and Method, Ch Monte Carlo and the bootstrap: uncertainty by sampling
Problem
A Monte Carlo simulation of the density of a glass marble, drawing its mass and diameter from their budget rows, gives a relative standard uncertainty of 0.95 per cent from B=1000 trials. A lab partner says: "Let's rerun it with B=106 trials; then we'll know the marble's density far better than 0.95 per cent."
((a)) Using the rule that a simulated standard deviation for a bell-shaped output is known to about 1/2B of itself, find how precisely the 0.95 per cent figure is known at B=1000 and at B=106, in percentage points.
((b)) Say whether increasing B from 1000 to 106 makes the density measurement itself more precise, and state what relative uncertainty should be quoted for the density at each value of B.