Track 13 · Resampling and Statistical Reasoning · Lesson 3 of 10
Monte Carlo simulation
Answer probability and method-checking questions by simulation, and quantify and control the Monte Carlo error of the answer.
Is a 95% confidence interval still a 95% interval when the data are skewed and the sample is small? The algebra is hard; a simulation answers it in seconds. But a simulation's answer is itself an estimate, and reporting 0.904 when the simulation can only resolve ±0.01 is false precision.
Monte Carlo simulation answers a question by building a model of the random process, running it many times on a computer, and summarising what happens. A probability becomes the proportion of runs in which the event occurs; an expected value becomes the average over runs.
You have already used it: the bootstrap and the Monte Carlo permutation test are both Monte Carlo methods. Here we use simulation more generally — to compute awkward probabilities and to check whether a statistical method does what it claims.
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It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Estimate a probability or an expected value by simulation from a stated model
- Compute the Monte Carlo standard error and report results to the precision it supports
- Plan the number of runs: four times the runs halve the error
- Use simulation to check whether a method keeps its promise (e.g. interval coverage)