Simulation models of scientific interest often lack a tractable likelihood function, precluding standard likelihood-based parameter inference. Consequently, it is often convenient to adopt approximate simulation-based inference procedures which seek to mimic conventional inference techniques using data simulated from the model. Popular simulation-based inference procedures include approximate Bayesian computation, where an approximate posterior is sampled by comparing simulator output and observed data through some notion of distance. They also include density ratio estimation, where probabilistic classifiers are employed to estimate the simulator’s likelihood-to-evidence ratio, permitting both frequentist and Bayesian inference. While such approaches are appealing, adapting them to high-dimensional data such as time-series can be challenging. In this talk, we will discuss how path signatures and the recently developed signature kernel can be employed in such approximate Bayesian inference procedures to flexibly accommodate time-series simulators. The talk will be based on joint work with Patrick Cannon and Sebastian M Schmon.
Joel is a final-year PhD student at the University of Oxford's Mathematical Institute and Institute for New Economic Thinking, and an Enrichment Student at the Alan Turing Institute and University of Bristol. He is broadly interested in the use of simulation and machine learning in the social sciences, particularly the use of agent-based models and in developing simulation-based inference procedures for generic time-series simulators.
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