Summary statistic construction by semi-automatic ABC
saABC fits parameter estimators based on simulated data to be
used as summary statistics within ABC. Fitting is by linear
regression. Some simple diagnostics are provided for assistance.
A n x d matrix or data frame of simulated parameter values.
A n x p matrix or data frame of simulated data and/or associated
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.
saABC function automates step 2 of this process. The user
must supply simulated parameter values
theta and corresponding
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.
Vector of constant terms from fitted regressions.
Matrix of weights from fitted regressions.
Vector of BIC values for each fitted regression.
Blum, M. G. B, Nunes, M. A., Prangle, D. and Sisson, S. A. (2013) A
comparative review of dimension reduction methods in approximate
Bayesian computation. Stat. Sci. 28, Issue 2, 189–208.
Fearnhead, P. and Prangle, D. (2012) Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation. J. R. Stat. Soc. B 74, Part 3, 1–28.
Nunes, M. A. and Prangle, D. (2016) abctools: an R package for tuning approximate Bayesian computation analyses. The R Journal 7, Issue 2, 189–205.
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