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Parametric statistical models that are implicitly defined in terms of astochastic data generating process are used in a wide range of scientificdisciplines because they enable accurate modeling. However, learning theparameters from observed data is generally very difficult because theirlikelihood function is typically intractable. Likelihood-free Bayesianinference methods have been proposed which include the frameworks ofapproximate Bayesian computation (ABC), synthetic likelihood, and its recentgeneralization that performs likelihood-free inference by ratio estimation(LFIRE). A major difficulty in all these methods is choosing summary statisticsthat reduce the dimensionality of the data to facilitate inference. Whileseveral methods for choosing summary statistics have been proposed for ABC, theliterature for synthetic likelihood and LFIRE is very thin to date. We hereaddress this gap in the literature, focusing on the important special case oftime-series models. We show that convolutional neural networks trained topredict the input parameters from the data provide suitable summary statisticsfor LFIRE. On a wide range of time-series models, a single neural networkarchitecture produced equally or more accurate posteriors than alternativemethods.

Dynamic Likelihood-free Inference via Ratio Estimation (DIRE)