**A**mong the flury of papers arXived around the ICML 2019 deadline, I read on my way back from Oxford a paper by Wiqvist et al. on learning summary statistics for ABC by neural nets. Pointing out at another recent paper by Jiang et al. (2017, Statistica Sinica) which constructed a neural network for predicting each component of the parameter vector based on the input (raw) data, as an automated non-parametric regression of sorts. Creel (2017) does the same but with summary statistics. The current paper builds up from Jiang et al. (2017), by adding the constraint that exchangeability and partial exchangeability features should be reflected by the neural net prediction function. With applications to Markovian models. Due to a factorisation theorem for d-block invariant models, the authors impose partial exchangeability for order d Markov models by combining two neural networks that end up satisfying this factorisation. The concept is exemplified for one-dimension g-and-k distributions, alpha-stable distributions, both of which are made of independent observations, and the AR(2) and MA(2) models, as in our 2012 ABC survey paper. Since the later is not Markovian the authors experiment with different orders and reach the conclusion that an order of 10 is most appropriate, although this may be impacted by being a ble to handle the true likelihood.

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