Archive for MA(q) model

a pen for ABC

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , on February 13, 2019 by xi'an

Among 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.

a survey on ABC

Posted in R, Statistics with tags , , , on January 7, 2011 by xi'an

With Jean-Michel Marin, Pierre Pudlo and Robin Ryder, we just completed a survey on the ABC methodology. It is now both arXived and submitted to Statistics and Computing. Rather interestingly, our first draft was written in Jean-Michel’s office in Montpelier by collating the ‘Og posts surveying new ABC papers! (Interestingly because this means that my investment in the ‘Og is now such that it needs to [and can] be recycled into papers and books. Another paper with Randal Douc is inspired from a reply to a comment…) Besides surveying the recent literature, this paper illustrates the behaviour of the ABC approximation in the simple case of the MA(2) model. Both graphs reproduced here illustrate the impact of the choice of the distance (above) and of the tolerance level (below, in a model choice setting).