Simulations

Synonyms

In probability modeling: Monte Carlo procedures, Random sampling with pseudo-random numbers. In statistical inference: Bootstraps, (simulated) permutation tests, Markov chain Monte Carlo (MCMC)

Glossary

Beta distributions:

The general density function is $f\left(x,\mid, \alpha,, \beta \right)=\frac{\varGamma \left(\alpha +\beta \right)}{\varGamma \left(\alpha \right)\varGamma \left(\beta \right)}{x}^{\alpha -1}{\left(1-x\right)}^{\beta -1},\,\,$

for 0 < x < 1 (0 otherwise). We denote a beta distribution by BETA(α,  β). Shape parameters: α > 0 ,  β > 0. Note: $\varGamma \left(1/2\right)=\sqrt{\pi }$ and, for positive integer k, Γ(k) = (k − 1)!

Bootstraping:

A method of statistical inference based on extensive simulation, often used to make confidence intervals. Takes a large number of resamples from the original data (or from a distribution suggested by them) to assess variability. Introduced by Efron (1979) and discussed in Efron and Tibshirani (1998)

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