Markov chain, hidden Markov model

Markov chain ：
Reference link ：
https://blog.csdn.net/weixin_42509541/article/details/123332839

My understanding of it is ：
The data is a set of discrete random variables .
The next time （t+1) The output of depends only on the current （t) The input of .
Its calculation has been based on the previous results , It's all probability models .
The example in the above link is well written .

hidden Markov model ：
I'm through 《 Statistical learning 》（ expericnce ） Learning through books , The writing is also very good .
Hidden Markov model is introduced here .

It needs to be clear State transition probability matrix , Observation probability matrix , The initial probability vector And so on .

The following example well explains this model .


Next is the probability calculation algorithm , It is divided into forward calculation and backward calculation .






Just read the pictures and links above carefully , I believe that the Markov chain (Markov Chain) And the hidden Markov model , If you want to know more , You need to check other information .
understand ：
For these models , It's easy to forget if you don't use it or review it often , My suggestion is to have a brief look at it if you have nothing to do , Review the old and learn the new , And the occasional review will bring good results . Accumulate this knowledge slowly .

What a long long road! , I will go up and down ！！！