posterior. Previous work has also considered how to weight or select summary statistics for ABC. @fearnhead2012constructing developed a popular method to find informative linear combinations of summary statistics by fitting a regression for each model parameter. Another successful approach is the subset selection method of @barnes2012considerate, which uses an approximate sufficiency criterion to select a subset of summary statistics on which to base inference. We explore these methods in further detail in Section \[DimReduction\].

A genetic algorithm has been used to choose the weights of different summary statistics [@jung2011choice]. This genetic algorithm attempts to optimize the mean squared error (MSE) of the posterior samples from the true parameter, however this is generally not known in practice. A method for adaptively choosing summary statistic weights for ABC based on the scale of the summary statistics has also been investigated [@prangle2015adapting]. The median absolute deviation, a measure of spread of a statistic, is used for the scaling. The aim is that all summary statistics contribute equally to the distance function. In practice, however, this may not be the most desirable choice, as some summary statistics are clearly more informative than others.

Recently, @singh2018multi have proposed a multi-armed bandit problem approach to selecting 