A spatio-temporal model for precipitation is presenteds. Modeling the
continuous and the discrete part of rainfall together, it is assumed that
precipitation has a censored and power-transformed normal distribution. The
mean of this distribution is linked to covariates. Spatio-temporal correlations
are accounted for by a latent Gaussian variable that follows a Markovian
temporal evolution combined with spatially correlated innovations. We propose
to specify the temporal evolution using a vector autoregression that is
motivated by an autoregressive convolution approach. Exploiting in a natural
way the unidirectional flow of time, the model allows for non-separable
covariance structures. Furthermore, the Markovian structure offers
computational benefits. The model is space as well as time resolution
consistent. We apply the model to three-hourly Swiss rainfall data, collected
at 26 stations. As a side result, we introduce a new tool, the primary
posterior predictive density, for assessing the fit of Bayesian models.