ABC in 1984

“Bayesian statistics and Monte Carlo methods are ideally suited to the task of passing many models over one dataset” D. Rubin, Annals of Statistics, 1984

Jean-Louis Foulley sent me a 1984 paper by Don Rubin that details in no uncertain terms the accept-reject algorithm at the core of the ABC algorithm! Namely,

Generate ;
Generate ;
Accept if

Obviously, ABC goes further by replacing the acceptance step with the tolerance condition

but this early occurence is worth noticing nonetheless. It is also interesting to see that Don Rubin does not promote this simulation method in situations where the likelihood is not available but rather as an intuitive way to understanding posterior distributions from a frequentist perspective, because ‘s from the posterior are those that could have generated the observed data. (The issue of the zero probability of the exact equality between simulated and observed data is not dealt with in the paper, maybe because the notion of a “match” between simulated and observed data is not clearly defined.) Apart from this historical connection, I recommend the entire paper as providing a very compelling argument for practical Bayesianism!