Neural Likelihood Approximation for Integer Valued Time Series Data
This addresses a problem for researchers in ecology and epidemiology by providing a simpler and faster inference method, though it is incremental as it builds on simulation-based approaches.
The paper tackled the challenge of inferring parameters for integer-valued time series models, where likelihoods are intractable, by constructing a neural likelihood approximation trained with unconditional simulations. The result showed accurate posterior approximations and significant computational speed-ups compared to existing methods.
Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations cannot be ignored and stochastic effects are important. The inference of the parameters of such models, from time series data, is challenging due to intractability of the likelihood. To work at all, current simulation based inference methods require the generation of realisations of the model conditional on the data, which can be both tricky to implement and computationally expensive. In this paper we instead construct a neural likelihood approximation that can be trained using unconditional simulation of the underlying model, which is much simpler. We demonstrate our method by performing inference on a number of ecological and epidemiological models, showing that we can accurately approximate the true posterior while achieving significant computational speed ups compared to current best methods.