There is some great info out there about algorithms like MCMC that are used for Bayesian statistical inference, and it's pretty approachable if you have a basic knowledge of statistics. What's interesting is that these methods build on the same math (gradients, matrix calculus, etc) that you'd need to understand for machine learning. Why not learn both while you're at it?
There's also the developing area of Bayesian deep learning, where the concepts of Bayesian inference and deep learning are brought together to create models that provide not just predictions but also the uncertainty that the model has in them. This is especially interesting to me because I've found it difficult to successfully apply ML to survey statistics: it's critical to provide confidence intervals for survey data and most ML tools don't support them without dubious methods.
So I'm excited about libraries like Edward (Bayesian tools built on TensorFlow), which have the potential to make this field a lot more accessible and scalable. It appears that Edward is being integrated into TensorFlow itself. This could be awesome because building on TensorFlow means you might be able to take advantage of things like TPUs, which would speed up these Bayesian algorithms significantly (in comparison to Stan, the de facto standard tool for Bayesian inference, which relies primarily on CPU execution).
Anyways, though I'm definitely late to this party, I'm still happy to be here.