Uncertainty of prior and posterior model probability: Implications for interpreting Bayes factors

In most applications of Bayesian model comparison or Bayesian hypothesis testing, the results are reported in terms of the Bayes factor only, not in terms of the posterior probabilities of the models. Posterior model probabilities are not reported because researchers are reluctant to declare prior model probabilities, which in turn stems from uncertainty in the prior. Fortunately, Bayesian formalisms are designed to embrace prior uncertainty, not ignore it. This article provides a novel derivation of the posterior distribution of model probability, and shows many examples. The posterior distribution is useful for making decisions taking into account the uncertainty of the posterior model probability. Benchmark Bayes factors are provided for a spectrum of priors on model probability. R code is posted at https://osf.io/36527/. This framework and tools will improve interpretation and usefulness of Bayes factors in all their applications.

A Continuous-Time Semi-Markov Model for Animal Movement in a Dynamic Environment

We consider an extension to discrete-space continuous-time models animal movement that have previously be presented in the literature. The extension from a continuous-time Markov formulation to a continuous-time semi-Markov formulation allows for the inclusion of temporally dynamic habitat conditions as well as temporally changing movement responses by animals to that environment. We show that with only a little additional consideration, the Poisson likelihood approximation for the Markov version can still be used within the multiple imputation framework commonly employed for analysis of telemetry data. In addition, we consider a Bayesian model selection methodology with the imputation framework. The model selection method uses a Laplace approximation to the posterior model probability to provide a computationally feasible approach. The full methodology is then used to analyze movements of 15 northern fur seal (Callorhinus ursinus) pups with respect to surface winds, geostrophic currents, and sea surface temperature. The highest posterior model probabilities belonged to those models containing only winds and current, SST did not seem to be a significant factor for modeling their movement.