Migration flow network reconstruction via approximate Bayesian computation

The field of network science has been growing steadily for the past two decades as a way to interpret relational data. Recovering missing information about a network is a task that researchers have to deal with frequently. We refer to this task as network reconstruction. Complex network data can also lead to situations where the likelihood function is intractable. Approximate Bayesian computation (ABC) is a class of algorithms that allows one to perform reliable inference without the need for a fully tractable likelihood function. Our efforts focus on reconstructing a network of migration flows using two ABC techniques. We use a log-linear gravity model as a way to estimate the flow counts in this network, as well as a Poisson distribution as a stochastic element. We use the expected values of each posterior distribution we obtain for each parameter in our model as point estimates in order to reconstruct a target matrix of EU countries. We employ a simulation study in order to validate this methodology and subsequently compare these results with two ground truth algorithms, one Bayesian and one deterministic, and discuss the potential of ABC techniques to be applied for this task.