Practice question · Put in order
Order the steps of estimating the area of an irregular shape by Monte Carlo.
- Generate many random points uniformly inside the rectangle
- Report the estimate together with its uncertainty
- Count how many of them fall inside the shape
- Enclose the shape in a rectangle whose area is known
- Multiply the rectangle's area by the fraction that fell inside
Hints
- You need a region of known area to sample from before you can sample.
- The final answer is a statistic, so it is incomplete without an error estimate.
Show the answer
- Enclose the shape in a rectangle whose area is known
- Generate many random points uniformly inside the rectangle
- Count how many of them fall inside the shape
- Multiply the rectangle's area by the fraction that fell inside
- Report the estimate together with its uncertainty
Why
The known enclosing area is what converts a counted fraction into an area. Reporting the uncertainty is part of the method, not an optional courtesy, without it the number claims a precision it does not have.
Practise Simulation and Monte Carlo Methods
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