What is an extremely quick resource to learn how to implement bayesian models in Python?

You mentioned that you know how to implement machine learning models in Matlab. This implies that you how machine learning algorithms are constructed. My feeling is that you are only finding it difficult because either you have not implemented Bayesian generative models or Generative models or you think there is something special about Python (actually there is none). I would start with how to implement generative models. When I did my first implementation, I was so scared. I searched a lot and I stumbled upon chapter 2 of Markov chain Monte Carlo in practice, all my confusions were dispelled. You must write equations with your hand, on the paper. Do it twice or thrice and you will  just "get it". Personally what I felt that every thing is in my mind. I hope this will help you to battle through first critical step "instilling confidence in yourself"  and rest is all easy. Now it means you have equations with you. Since we are talking about generative models either you have some data or you want to generate some "dummy data". If you  have data good, if you don't, you need to generate data using you generative process.  Remember generative process is the assumption that you know how data came, and all you want is to learn the parameters.  There are many ways to go for it. Free all the parameters while generating data, or few of them so that you can pinpoint mistakes of your code. I could discuss more about, but for now, this should be enough. Decide upon prior, I generally tend to start with non informative prior, loosely means you want to play safe and assume that uniform probability (here I would like the experts to comment). Write functions for each model parameters. Now you have parameters, prior, data. You want to  add few more utility stuffs like logging, something which takes backup of model after lets say 1 hour etc. All I mean to say, at times model run for long time, sometimes you might want to stop, check something etc. Also you want to have some way to decide when to stop. This is really difficult question,  what I personally do is plat the variable and see if they are converging to some value, Smart guy like you would probably write a script or thread which would analyze dumped model parameters and may send a signal when to stop. Some folks suggest using Rao-Blackwill theorem to decide when to stop, but I have never tried. Please let me know if you do so.  So you have every thing needed to run the code.  Aha, I didn't talk about sampling. I tend to use Gibbs sampler and rejection sampler. Do the standard stuffs like computations in log-space, caching/smart updates, drop the constant part. Also do understand under optimization library. If the problem is with python. Then learn about random number generators (normal, gamma etc...), optimization library (may be pyGSL), read/write data (many people would suggest Panda), matplotlib to plot convergence. I think this is all you need. 3. Most important thing is first step. If you take you take your first step, every thing just happen magically.  Only the courage to take first step holds us back. ATB

You can try PySTAN (https://pystan.readthedocs.org/en/latest/) which allows to easily define complex hierarchical bayesian models using many different types of Monte Carlo estimations including fancy Hamiltonean MC.