As hedge fund replication based on factor models has encountered growing interest among professionals and academics, and despite the launch of numerous products (indexes and mutual funds) in the past year, it faced many critics. In this paper, we consider three of the main critiques, namely the lack of reactivity of hedge fund replication and its deficiency in capturing tactical allocations; its failure to apprehend non-linear positions of the underlying hedge fund industry and higher moments of hedge fund returns; and, finally, the lack of access to the alpha of hedge funds. To address these problems, we consider hedge fund replication as a general tracking problem which may be solved by means of Bayesian filters. Using the linear Gaussian model as a basis for discussion, we provide the reader with an intuition for the inner tenets of the Kalman filter and illustrate the results' sensitivity to the algorithm specification choices. This part of the paper includes considerations on the type of strategies which can be replicated, as well as the problem of selecting factors. We then apply more advanced Bayesian filters' algorithms, known as particle filters, to capture the non-normality and non-linearities documented on hedge fund returns. Finally, we address the problem of accessing the pure alpha by proposing a core/satellite approach of alternative investments between high-liquid alternative beta and less liquid investments.