Wish life was at least as explicable as The HMM,

But alas! It's even more complex.

You may understand The HMM one day,

But not your life and interactions.

In probability & statistics,
A Markov chain or Markoff chain or a Markov Process,
Named after the Russian mathematician Andrey Markov,
Is a stochastic process that satisfies the Markov property
And is usually characterized as "memorylessness".

Imagine an urn experiment with replacement,
Hidden Markov Model can be visualized likewise.

Consider a hidden room with a genie inside,
The room has N urns with n ***** in each.

The genie chooses an urn in that room,
He randomly draws a ball from the urn.

He then puts the ball onto a conveyor belt,
Which is being observed for the sequence,
Only the ***** on the conveyor are visible,
Not the urns from which they were drawn.

The genie has a procedure to choose urns,
The choice of the urn for the n-th ball,
It depends only upon a random number,
And the choice of the urn for the (n − 1)-th ball.

The choice of urn does not directly depend on
The urns chosen before this single previous urn;
Therefore, this is called a Markov process.

*Hidden Markov models model complex Markov processes,
Where the states emit the observations according to a distribution.
One such example is a Gaussian distribution,
In such a Hidden Markov Model,
The state's output are represented by a Gaussian distribution.