Dynamic Likelihood-free Inference via Ratio Estimation (DIRE)
This addresses a gap in the literature for synthetic likelihood and LFIRE methods, specifically for time-series models, though it is incremental as it adapts existing neural network techniques to a known bottleneck.
The paper tackled the challenge of selecting summary statistics for likelihood-free inference in time-series models, showing that convolutional neural networks trained to predict parameters from data provide effective statistics, leading to equally or more accurate posteriors than alternative methods across a range of models.
Parametric statistical models that are implicitly defined in terms of a stochastic data generating process are used in a wide range of scientific disciplines because they enable accurate modeling. However, learning the parameters from observed data is generally very difficult because their likelihood function is typically intractable. Likelihood-free Bayesian inference methods have been proposed which include the frameworks of approximate Bayesian computation (ABC), synthetic likelihood, and its recent generalization that performs likelihood-free inference by ratio estimation (LFIRE). A major difficulty in all these methods is choosing summary statistics that reduce the dimensionality of the data to facilitate inference. While several methods for choosing summary statistics have been proposed for ABC, the literature for synthetic likelihood and LFIRE is very thin to date. We here address this gap in the literature, focusing on the important special case of time-series models. We show that convolutional neural networks trained to predict the input parameters from the data provide suitable summary statistics for LFIRE. On a wide range of time-series models, a single neural network architecture produced equally or more accurate posteriors than alternative methods.