The semi-automatic ABC method of Fearnhead and Prangle (2012) is as
follows: 1) Simulate parameter vectors $\theta_i$ and corresponding data sets $x_i$ for i=1,2,...,N.
2) Use the simulations to fit an estimator of each parameter as a
linear combination of f(x), where f(x) is a vector of
transformations of x (including a constant term).
3) Run ABC using these simulations.
The saABC function automates step 2 of this process. The user
must supply simulated parameter values theta and corresponding
f(x) values x (n.b. excluding the constant term). The function
returns weights for the linear combinations which can easily be used
for step 3. In particular, fitted weights are returned as a matrix
of weights for the columns of x and a vector of constants. The
vector can usually be discarded, as it is not needed to find
differences between summary statistics.
The function also returns BIC values for each parameter so that the
user can judge the quality of the fits, and compare different choices
of f(x). Diagnostic plots of supplied parameter values against fitted
values are also optionally provided. These are useful for exploratory
purposes when there are a small number of parameters, but provide less
protection from overfitting than BIC values.