Daniel Simpson

Abstract: In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys’ priors, are designed to support Occam’s razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations.

TL;DR: A new concept for constructing prior distributions that is invariant to reparameterisations, have a natural connection to Jeffreys’ priors, seem to have excellent robustness properties, and allow this approach to define default prior distributions.

TL;DR: The INLA approach for approximate Bayesian inference for latent Gaussian models has been shown to give fast and accurate estimates of posterior marginals and to be a valuable tool in practice via the R-package R-INLA.

TL;DR: Integrated nested Laplace approximations (INLA) as mentioned in this paper approximates the integrand with a second-order Taylor expansion around the mode and computes the integral analytically.

TL;DR: Visualization is helpful in each of these stages of the Bayesian workflow and it is indispensable when drawing inferences from the types of modern, high dimensional models that are used by applied researchers.