Scientific models described by computer simulators often lack a tractable likelihood function, precluding the use of standard likelihood-based statistical inference.
A plethora of statistical and machine learning approaches have been developed to tackle this problem, such as approximate Bayesian computation and likelihood/posterior approximations. What those methods have in common is the aim to connect real world data with parameters of the underlying simulator.
However, effective measures that can link simulated and observed data are generally difficult to construct, particularly for time series data which are often high-dimensional and structurally complex. In this talk, we discuss the use of path signatures as a natural candidate feature set for constructing summary statistics and distances between time series data for use in simulation-based inference algorithms, for example in approximate Bayesian computation. Our experiments show that such an approach can generate more accurate approximate Bayesian posteriors than existing techniques for time series models.
zoom link: https://durhamuniversity.zoom.us/j/93730370636?pwd=T2V4ekkvai95K2paSlNqV21IMXRWUT09