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Title: Identifying relations between summary statistics and parameters in ABC: A network approach Authors:  Yangqi Zhang - The University of New South Wales (Australia) [presenting]
Valentyn Panchenko - Univerisity of New South Wales (Australia)
Abstract: Likelihood-free methods such as approximate Bayesian computation (ABC) are popular tools to perform inference for complex models by simulation when the likelihood is intractable. Summary statistics are used for parameter inference in ABC. The choice of summary statistics often relies on prior knowledge or intuition. A novel network approach is proposed to identify and visualise the relations between the summary statistics and parameters of interest in ABC. After a pilot ABC process, pairwise partial correlations among summary statistics and parameters are computed and visualised as a weighted network of parameters and summary statistics. The resulting network is then pruned using network filtering and communication detection techniques. Such a network can improve the overall ABC performance, especially in high-dimensional settings. The authors also discuss the relationship between the network approach and other summary statistics selection techniques in ABC literature. Furthermore, the network provides information on decomposing complex models into several coupled modules. The decomposition is useful to the ``cutting feedback'' method, which provides robust inference when the model is misspecified. The performance of the network method is demonstrated in several simulated and real examples.