Theoretical foundations of approximate Bayesian computation

2015-04-23We introduce Monte Carlo estimates with discussion of numerical integration and the curse of dimensionality, using a toy example of estimating π using a d−dimensional hyper‐sphere embedded in a d−dimensional unit hyper‐cube. Some common Monte Carlo methods such as Rejection Sampling, Markov chain Monte Carlo, Importance Sampling, and Sequential Monte Carlo are then discussed. We follow with an introduction to a type of Bayesian inference known as Approximate Bayesian Computation (ABC), and apply each of our discussed Monte Carlo algorithms in ABC terms, ultimately arguing that Sequential Monte Carlo methods are best suited for ABC