The f-electron materials (lanthanides and actinides) exhibit a rich array of strongly correlated electron phenomena. Most notable are their anti-ferromagnetism and frequent heavy fermion behaviors. They are generally mixed valence materials. Traditionally, the periodic Anderson model is used to describe the behavior of these materials, and mean-field and variational analyses of this model have lead to the picture that the magnetic properties of the materials are a result of a competition between the RKKY and the Kondo interactions. I will report the results of recent quantum Monte Carlo studies of this model in the mixed-valence regime that find itinerant ferromagnetism to be the dominant magnetic state and that this state does not arise because of the RKKY interaction. I will also report that in the non-magnetic state the compensation of the local f-electron magnetic moments is mainly caused by correlations that develop among the f-electrons and not by correlations between the d and f electrons as implied by a Kondo-like compensation. The relevance of the results of the simulation to the unusual magnetic properties of some ferromagnetic Ce compounds will be illustrated.