collection of summaries can be used and weighted appropriately via our procedure. It is also possible to combine our framework with existing dimensionality reduction techniques for summary statistics in ABC (see Section \[DimReduction\]).

We outline in Section \[weights\_algorithm\] our adaptive algorithm for combining summary statistics in an ABC framework. We provide theoretical justification for the algorithm in Section \[justification\] and demonstrate that, in the appropriate limit, we obtain convergence to the posterior distribution. To demonstrate the utility of our algorithm, we apply it to several test problems based on biochemical reaction networks in Section \[Examples\]. We compare results of parameter inference using our algorithm against benchmark results from applying ABC-SMC using other choices of weights for the summary statistics. Finally, in Section \[Summary\], we summarize the work presented in this article and compare our methodology for combining summary statistics with other techniques in the literature that are based on dimensionality reduction of a set of summary statistics.

An algorithm for automatic weighting of summary statistics {#weights_algorithm}
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In order to use ABC-SMC (see Algorithm 1), we must specify a function to measure the distance between simulated and real datasets. Suppose we take a weighted Euclidean distance as our ABC distance 