Bayesian analysis of a density ratio model

This work proposes a Bayesian approach for the analysis of a semiparametric density ratio model, a model useful for the integration of data from multiple sources. The proposed Bayesian analysis uses a non‐parametric likelihood and a transformed Gaussian prior for the “non‐parametric part” of the model. The former choice guarantees the validity of the Bayesian analysis in contrast to some semiparametric Bayesian analyses that rely on empirical likelihoods whereas the latter choice allows the representation of an expected smoothness property. We describe a Markov chain Monte Carlo algorithm to fit this model which was found to empirically display good convergence behaviour. The model is illustrated with the analysis of motor vibration data obtained from three different locations on a motor. The Canadian Journal of Statistics 45: 274–289; 2017 © 2017 Statistical Society of Canada