Informed Bayesian finite mixture models via asymmetric Dirichlet priors

There is keen interest in the field of biomechanics to identify unique strategies of negotiating specific movement tasks post lower-limb joint injury. Finite mixture models are flexible methods that are commonly used for carrying out this type of task. A recent focus in the model-based clustering literature is to highlight the difference between the number of components in a mixture model and the number of clusters. The number of clusters is more relevant from a practical stand point, but to date, the focus of prior distribution formulation has been on the number of components. This can make prior elicitation on the number of clusters challenging when prior information exists, which is the case in the biomechanic study considered here. In light of this, we develop a finite mixture methodology that permits eliciting prior information directly on the number of clusters in a flexible and intuitive way. This is done by employing an asymmetric Dirichlet distribution as a prior on the weights of a finite mixture. Further, a penalized complexity motivated prior is employed for the Dirichlet shape parameter. We illustrate the ease to which prior information can be elicited via our construction and the flexibility of the resulting induced prior on the number of clusters. In addition to applying the method to the biomechanic data, we also demonstrate utility using numerical experiments and the galaxies dataset.