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Abstract
Bayesian inference and Markov chain Monte Carlo techniques have enjoyed enormous popularity since they were introduced into phylogenetics about a decade ago. We provide an overview of the field, with emphasis on recent developments of importance to empirical systematists. In particular, we describe a number of recent advances in the stochastic modeling of evolution that address major deficiencies in current models in a computationally efficient way. These include models of process heterogeneity across sites and lineages, as well as alignment-free models and model averaging approaches. Many of these methods should find their way into standard analyses in the near future. We also summarize the influence of Bayesian methods on insect systematics, with particular focus on current practices and how they could be improved using existing and emerging techniques.