  Assessing the magnitude of fuel consumption of marine traffic is a
challenging task. The consumption can be reduced by the ways the vessels are
operated, to achieve both improved cost efficiency and reduced CO2 emissions.
Mathematical models for predicting ships' consumption are in a central role in
both of these tasks. Nowadays, many ships are equipped with data collection
systems, which enable data-based calibration of the consumption models.
Typically this calibration procedure is carried out independently for each
particular ship, using only data collected from the ship in question. In this
paper, we demonstrate a hierarchical Bayesian modeling approach, where we fit a
single model over many vessels, with the assumption that the parameters of
vessels of same type and similar characteristics (e.g. vessel size) are likely
close to each other. The benefits of such an approach are two-fold; 1) we can
borrow information about parameters that are not well informed by the
vessel-specific data using data from similar ships, and 2) we can use the final
hierarchical model to predict the behavior of a vessel from which we don't have
any data, based only on its characteristics. In this paper, we discuss the
basic concept and present a first simple version of the model. We apply the
Stan statistical modeling tool for the model fitting and use real data from 64
cruise ships collected via the widely used commercial Eniram platform. By using
Bayesian statistical methods we obtain uncertainties for the model predictions,
too. The prediction accuracy of the model is compared to an existing data-free
modeling approach.
