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Probabilistic and set-based methods are two approaches for modelinvalidation, parameter and state estimation. Both classes of methods usedifferent types of data, i.e. deterministic or probabilistic data, which allowdifferent statements and applications. Ideally, however, all available datashould be used in estimation and model invalidation methods. This paperpresents an estimation and model invalidation framework combining set-based andprobabilistically uncertain data for polynomial continuous-time systems. Inparticular, uncertain data on the moments and the support is used without theneed to make explicit assumptions on the type of probability densities. Thepaper derives pointwise-in-time outer approximations of the moments of theprobability densities associated with the states and parameters of the system.These approximations can be interpreted as guaranteed confidence intervals forthe moment estimates. Furthermore, guaranteed bounds on the probability masseson subsets are derived and allow an estimation of the unknown probabilitydensities. To calculate the estimates, the dynamics of the probabilitydensities of the state trajectories are found by occupation measures of thenonlinear dynamics. This allows the construction of an infinite-dimensionallinear program which incorporates the set- and moment-based data. This linearprogram is relaxed by a hierarchy of LMI problems providing, as shownelsewhere, an almost uniformly convergent sequence of outer approximations ofthe estimated sets. The approach is demonstrated with numerical examples.

Probabilistic and Set-based Model Invalidation and Estimation using LMIs