Approximate Bayesian Computation (ABC)

Motivation/ use

A way to use simulation techniques to find the posterior distribution of a Bayesian model. It is especially useful when the likelyhood function is very complex, or cannot be fully specified or sampled from. In this case, the general posterior simulation techniques will not work.

Algorithm

  1. From basically any distribution draw
  2. Using , simulate data .
  3. Using a matching algorithm or summary statistic , check if where is a tolerance level. If it is, then keep the value, else reject it.
  4. Repeat a lot.

Resources

@rubin1984