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The increased immigration in Western Europe has been linked by some political parties to increased criminality rates. We study the statistical relationship between the proportion of foreign-born to three types of reported criminality - rapes, burglary, and assault. The analysis is based on Swedish municipality level data for 2002-2014, years with signicant immigration. Using non-parametric Gaussian processes models, we find that while reported rape rates have increased, they are likely best explained by changes in reporting. The reported burglary rates have decreased, while reported assault rates are positively correlated to the proportion of foreign-born residents in the municipality.

Social and economic systems produce complex and nonlinear relationships in the indicator variables that describe them. We present a Bayesian methodology to analyze the dynamical relationships between indicator variables by identifying the nonlinear functions that best describe their interactions. We search for the 'best' explicit functions by fitting data using Bayesian linear regression on a vast number of models and then comparing their Bayes factors. The model with the highest Bayes factor, having the best trade-off between explanatory power and interpretability, is chosen as the 'best' model. To be able to compare a vast number of models, we use conjugate priors, resulting in fast computation times. We check the robustness of our approach by comparison with more prediction oriented approaches such as model averaging and neural networks. Our modelling approach is illustrated using the classical example of how democracy and economic growth relate to each other. We find that the best dynamical model for democracy suggests that long term democratic increase is only possible if the economic situation gets better. No robust model explaining economic development using these two variables was found.