Prior for flexibility parameters : the Student

Extending a basic statistical model can be carried out by using a parametric family of distributions that contains the basic model as a particular case but has an extra parameter, which we denote by flexibility parameter, to control the amount of flexibility or deviation from the basic model. We propose a formal framework to construct prior distributions for the flexibility parameter that place the basic model in a central position within the flexible model, and allow the user to intuitively control the amount of flexibility around the basic model. We propose to assign a prior distribution to the divergence between the basic and the flexible model that encodes the centrality of the basic model within the flexible model. We apply our framework to relax a model based on Gaussian assumptions by extending it to a model based on the Student’s t distribution. In this case the flexibility parameter is the degrees of freedom of the Student’s t distribution. We show that our priors are robust with respect to its hyperparameters and give sensible results across many different scenarios. We also discuss disadvantages of using priors that do not place the basic model in a central position within the flexible model. Our framework to construct priors for the flexibility parameter is not restricted to the Student’s t case and can be applied to a variety of models that can be seen as an extension of a basic model.