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Stochastic processes defined on integer valued state spaces are popularwithin the physical and biological sciences. These models are necessary forcapturing the dynamics of small systems where the individual nature of thepopulations cannot be ignored and stochastic effects are important. Theinference of the parameters of such models, from time series data, is difficultdue to intractability of the likelihood; current methods, based on simulationsof the underlying model, can be so computationally expensive as to beprohibitive. In this paper we construct a neural likelihood approximation forinteger valued time series data using causal convolutions, which allows us toevaluate the likelihood of the whole time series in parallel. We demonstrateour method by performing inference on a number of ecological andepidemiological models, showing that we can accurately approximate the trueposterior while achieving significant computational speed ups in situationswhere current methods struggle.

Neural Likelihood Approximation for Integer Valued Time Series Data