by Aki Vehtari, Andrew Gelman, David B. Dunson, Donald B. Rubin, Hal S. Stern, John B. Carlin
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Suggested foundations for probability and statistical reasoning and monte carlo and numerical simulation. Specialist prerequisites vary by resource.
Read the distributions and expectations used in probabilistic arguments.
Interpret expectations after information is observed.
Understand convergence, sampling error and confidence intervals.
Generate reproducible samples and distinguish randomness from model assumptions.
Assess uncertainty rather than treating an estimate as a fact.
Turn a discounted payoff into an estimator.
Study dependence and alternatives to independent sampling.
Move from conditioning and expected values to timed problems with a defensible solution.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.