https://github.com/krasserm/bayesian-machine-learning

• a collection of notebooks about Bayesian Machine Learning.

https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-optimization/bayesian_optimization.ipynb

• Implementation with plain NumPy/SciPy as well as with libraries scikit-optimize and GPyOpt.
• Hyper-parameter tuning as application example.

probabilistic graphical model (PGM):
a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning.

Two branches of graphical representations of distributions are commonly used, namely, Bayesian networks and Markov random fields.

Plate notation:
a method of representing variables that repeat in a graphical model.
Instead of drawing each repeated variable individually, a plate or rectangle is used to group variables into a subgraph that repeat together, and a number is drawn on the plate to represent the number of repetitions of the subgraph in the plate. The assumptions are that the subgraph is duplicated that many times, the variables in the subgraph are indexed by the repetition number, and any links that cross a plate boundary are replicated once for each subgraph repetition.