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Abstract. We consider a stochastic differential equation modelfor Earth's axial magnetic dipole field.Our goal is to estimate the model's parametersusing diverse and independent data sources that had previously been treated separately,so that the model is a valid representation of an expanded paleomagnetic recordon kyr to Myr timescales.We formulate the estimation problem within the Bayesian frameworkand define a feature-based posterior distributionthat describes probabilities of model parameters givena set of features derived from the data.Numerically, we use Markov chain Monte Carlo (MCMC)to obtain a sample-based representation of the posterior distribution.The Bayesian problem formulation and its MCMC solutionallow us to study the model's limitations and remaining posterior uncertainties.Another important aspect of our overall approach is thatit reveals inconsistencies between model and data or within the various data sets.Identifying these shortcomings is a first and necessary step towards building more sophisticated models or towards resolving inconsistencies within the data.The stochastic model we derive representsselected aspects of the long-term behavior of the geomagnetic dipole fieldwith limitations and errors that are well defined.We believe that such a model is useful (besides its limitations) for hypothesis testing and give a few examples of how the model can be used in this context.