In this paper we introduce a statistical inference framework for estimating the contagion source from a partially observed contagion spreading process on an arbitrary network structure. The framework is based on a maximum likelihood estimation of a partial epidemic realization and involves large scale simulation of contagion spreading processes from the set of potential source locations. We present a number of different likelihood estimators that are used to determine the conditional probabilities associated to observing partial epidemic realization with particular source location candidates. This statistical inference framework is also applicable for arbitrary compartment contagion spreading processes on networks. We compare estimation accuracy of these approaches in a number of computational experiments performed with the SIR (susceptible-infected-recovered), SI (susceptible-infected) and ISS (ignorant-spreading-stifler) contagion spreading models on synthetic and real-world complex networks.The structure of vast majority of biological networks (biochemical, ecological), technological networks (internet, transportation, power grids), social networks and information networks (citation, WWW) can be represented by complex networks [16], [7], [3]. Epidemic or contagion processes are amongst the most prevalent type of dynamic processes of interest characteristic for these real-life complex networks and they include disease epidemics, computer virus spreading, information and rumor propagation [23]. Different mathematical frameworks have been used to study epidemic spreading. We can divide them into two major categories based upon assumptions they make: the homogeneous mixing framework and the heterogeneous mixing framework. The homogeneous mixing framework assumes that all individuals in a population have an equal probability of contact. This is a traditional mathematical framework [12], [10] in which differential equations are used to model epidemic dynamics. The heterogeneous mixing framework assumes * Corresponding author. Adress: Rudjer Bošković Institute,