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Soot from combustion processes often takes the form of fractal-like aggregates, assembled of primary particles, both of which obey polydisperse size distributions. In this work, the possibility of determining the primary particle size distribution through time-resolved laser-induced incandescence (TiRe-LII) under the influence of thermal shielding of polydispersely distributed aggregates is critically investigated for two typical measurement situations: in-flame measurements at high temperature and a soot-laden aerosol at room temperature. The uncertainty attached to the quantities is evaluated through Bayesian inference. We show how different kinds of prior knowledge concerning the aggregation state of the aerosol affect the uncertainties of the recovered size distribution parameters of the primary particles. To obtain reliable estimates for the primary particle size distribution parameters, specific information about the aggregate size distribution is required. This is especially the case for cold bath gases, where thermal shielding has a large effect. Furthermore, it is crucial to use the full duration of the usable LII signal trace to recover the width of the size distribution with small uncertainties. The uncertainty attached to TiRe-LII inferred primary particle size parameters becomes considerably larger when additional model parameters are considered.