Main articles:

• Yarin Gal's paper on drop out as bayesian approximation arxiv:1506.02142
• More informal blog post by Yarin Gal on the topic here

As always, an acompanying video:

• Yarin's presentation on the paper here
• Longer video of Yarin's presentation at Microsoft on Bayesian Deep Learning here

Additional resources:

• Yarin Gal's thesis is an extremely interesting read, summarising many developments in probabalistic approaches towards deep learning, as well as applications of uncertainty in predictions in Active Learning, Reinforcement learning etc. here