BayesPy is an open-source Python software package for performing variational Bayesian inference. It is based on the variational message passing framework and supports conjugate exponential family models. By removing the tedious task of implementing the variational Bayesian update equations, the user can construct models faster and in a less error-prone way. Simple syntax, flexible model construction and efficient inference make BayesPy suitable for both average and expert Bayesian users. It also supports some advanced methods such as stochastic and collapsed variational inference.

We present a probabilistic latent factor model which can be used for studying spatio-temporal datasets. The spatial and temporal structure is modeled by using Gaussian process priors both for the loading matrix and the factors. The posterior distributions are approximated using the variational Bayesian framework. High computational cost of Gaussian process modeling is reduced by using sparse approximations. The model is used to compute the reconstructions of the global sea surface temperatures from a historical dataset. The results suggest that the proposed model can outperform the state-of-the-art reconstruction systems.