'Ruth E. Baker'
bibliography:
- 'TT18.bib'
date: 'Received: date / Accepted: date'
title: An automatic adaptive method to combine summary statistics in approximate Bayesian computation 
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Introduction
============

When using quantitative models to explore biological or physical phenomena, it is crucial to be able to estimate parameters of these models and account appropriately for uncertainty in both the parameters and model predictions. Bayesian statistics offers a wealth of tools in this regard [@hines2015primer; @wilkinson2009stochastic]. Bayes’ theorem gives us that the posterior, $p(\theta | D)$, of parameters, $\theta$, given data, $D$, is proportional to a prior, $\pi(\theta)$, on the parameters multiplied by the likelihood, $p(D| \theta)$, of data, $D$, given those parameters: $p(\theta | D) \propto p(D|\theta) p(\theta)$. The prior represents our beliefs about the parameters prior to observing the data, the likelihood gives the probability of observing the data, given a certain set of parameters, and these result in the posterior, which returns updated beliefs about the parameters after having observed the data.

However, much of the current theory surrounding the generation of posterior distributions 