We present an new sequential Monte Carlo sampler for coalescent based Bayesian hierarchical clustering. Our model is appropriate for modeling non-i.i.d. data and offers a substantial reduction of computational cost when compared to the original sampler without resorting to approximations. We also propose a quadratic complexity approximation that in practice shows almost no loss in performance compared to its counterpart. We show that as a byproduct of our formulation, we obtain a greedy algorithm that exhibits performance improvement over other greedy algorithms, particularly in small data sets. In order to exploit the correlation structure of the data, we describe how to incorporate Gaussian process priors in the model as a flexible way to model non-i.i.d. data. Results on artificial and real data show significant improvements over closely related approaches.
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