Bayesian inference of spatial and temporal relations in AI patents for EU countries

In the paper, we propose two models of Artificial Intelligence (AI) patents in European Union (EU) countries addressing spatial and temporal behaviour. In particular, the models can quantitatively describe the interaction between countries or explain the rapidly growing trends in AI patents. For spatial analysis Poisson regression is used to explain collaboration between a pair of countries measured by the number of common patents. Through Bayesian inference, we estimated the strengths of interactions between countries in the EU and the rest of the world. In particular, a significant lack of cooperation has been identified for some pairs of countries. Alternatively, an inhomogeneous Poisson process combined with the logistic curve growth accurately models the temporal behaviour by an accurate trend line. Bayesian analysis in the time domain revealed an upcoming slowdown in patenting intensity.