important. This issue of comparing high-dimensional data is further compounded using stochastic models where there is noise in the process model in addition to measurement noise. Repeatedly drawing from a stochastic model with the same parameter values can give vastly different outputs.

As such, it is often necessary to work with a lower-dimensional vector of summary statistics, $s(\mathbf{x})$, of the data, such that we require the distance between summary statistics is less than the tolerance, $d(s(\mathbf{x^*}),s(\mathbf{y})) < \epsilon$. Examples of these summary statistics may be data points within a time series, an average transition time between different states of a system, or the moments of a certain species within a model. However, not all summary statistics are equally informative about the posterior. Common practice is to combine summary statistics based on some heuristic approach, such as the weighting the contribution of each summary statistic according to its standard deviation. However, it is not clear whether these heuristic approaches result in optimal weighting of the various summary statistics available. As such, the aim of this work is to provide an automated and adaptive method for determining the weighting of available summary statistics in order to optimize the quality of the resulting 