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Sparsity of data may complicate the analysis of historical earthquakes at every stage. Intensities are estimated on the basis of written documentary materials of various provenance and purpose, uncovered in archives and libraries. Modest amounts of textual information cannot be critically collated. Inadequate or skewed documentation of earthquake effects, and poor survival of documents to the present time, lead to uncertain intensities or only descriptive notations. Written documents and earthquake parameters may appear incompatible, but parameters are customarily derived for historical earthquakes when compiling parametric earthquake catalogues. The main focus of the presentation is on the parameters of historical earthquakes that are derived on the basis of sparse sets of intensity data. Here sparsity means few intensity data points per earthquake. The accuracy of parameters is important input for studies of regional seismotectonics and seismic hazard. Extensive simulations have been carried out to obtain insight into the topic.