Palaeoclimate reconstructions are based on the relationship between climate and sediment pollen assemblages. This model is called the transfer function (TF). Process-based TF emerge as an opportunity to better quantify past climate changes. For example, when a process-based model of vegetation dynamics is part of the TF it allows to include atmospheric CO2 concentration and plant-plant interactions as factors affecting the reconstruction. We propose the missing piece for a fully process-based TF: the model linking, at a continental scale, vegetation model outputs and pollen sampled in sediments. We perform its calibration and we explore the quality of fit. The model represents the error of the vegetation model LPJ-GUESS and four main processes: pollen production, dispersal, accumulation and sampling. Accumulation and sampling processes are either modelled using a multinomial-Poisson (MP) or a multinomial-negative binomial (MNB) model, both models allowing for overdispersion and structural zeros in the sense of null multinomial probabilities. We perform inference for a European pollen dataset by parallelising a Monte Carlo Markov Chain algorithm. Model fitness diagnostics indicate that MP model is not supported by the European dataset. The MNB model is also detected inconsistent, but with a p-value of 0.014 and without stationarity nor overdispersion problems. At this stage, the MNB model is considered as a robust alternative to more complex models. We finally discuss the challenge of the TF inversion for palaeoclimate reconstruction and vegetation model re-calibration.