Hidden Markov Model -- Implemented from scratch

The Internet is full of good articles that explain the theory behind the Hidden Markov Model (HMM) well (e.g. 1, 2, 3 and 4). However, many of these works contain a fair amount of rather advanced mathematical equations. While equations are necessary if one wants to explain the theory, we decided to take it to the next level and create a gentle step by step practical implementation to complement the good work of others. In this short series of two articles, we will focus on translating all of the complicated mathematics into code. Our starting point is the document written by Mark Stamp.