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In this work we use variational inference to quantify the degree of uncertainty in deep learning model predictions of radio galaxy classification. We show that the level of model posterior variance for individual test samples is correlated with human uncertainty when labelling radio galaxies. We explore the model performance and uncertainty calibration for different weight priors and suggest that a sparse prior produces more well-calibrated uncertainty estimates. Using the posterior distributions for individual weights, we demonstrate that we can prune 30 per cent of the fully connected layer weights without significant loss of performance by removing the weights with the lowest signal-to-noise ratio. A larger degree of pruning can be achieved using a Fisher information based ranking, but both pruning methods affect the uncertainty calibration for Fanaroff–Riley type I and type II radio galaxies differently. Like other …