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leonard zinovyev May 2019
Tyger! Tyger! pants on fire.
Pants on fire, burning bright.
And what chain, & what art?
What the sinew? what the *?

Markov! Markov! chains on fire.
On what wings does he aspire?
And what hand at a rapid rate
Dare ‘em hastily generate?

In the forests burning bright,
In the distant deeps and skies.
Lo ‘n’ behold! what a symmetry!
Did he smile his work to see?

Tyger! Tyger! pants on fire.
Pants on fire, burning bright.
And what chain, & what art?
What the sinew? what the *

Python! Python! Monte Carlo,
The chain order is so low.
Product placement detected!
Your PC may be infected!
Àŧùl Dec 2016
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.
References: Wikipedia.

A Hidden Markov Model (HMM) is a statistical Markov model in which the system being modelled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be presented as the simplest dynamic Bayesian network.

For revising an important topic from bioinformatics.

HP Poem #1298
©Atul Kaushal

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