https://github.com/danielhanchen/reversing_markov_chains

Sometimes we want to ”reverse” a Markov Chain process. Taking the inverse of the transition matrix allows this to work, but the inverse result is not a transition matrix. If I wanted to model a population going to work, and then going back home, negative and greater than 1 probabilities in the inverse matrix will cause issues. I propose a method to compute the ”inverse” of a transition matrix, and the result is still a transition matrix
https://github.com/danielhanchen/reversing_markov_chains

inverse markov-chain markov-model matrix

Last synced: 8 days ago
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Sometimes we want to ”reverse” a Markov Chain process. Taking the inverse of the transition matrix allows this to work, but the inverse result is not a transition matrix. If I wanted to model a population going to work, and then going back home, negative and greater than 1 probabilities in the inverse matrix will cause issues. I propose a method to compute the ”inverse” of a transition matrix, and the result is still a transition matrix

• Host: GitHub
• URL: https://github.com/danielhanchen/reversing_markov_chains
• Owner: danielhanchen
• License: mit
• Created: 2017-11-11T12:09:20.000Z (about 7 years ago)
• Default Branch: master
• Last Pushed: 2017-11-11T12:22:44.000Z (about 7 years ago)
• Last Synced: 2024-10-28T12:02:44.039Z (about 2 months ago)
• Topics: inverse, markov-chain, markov-model, matrix
• Language: Python
• Size: 139 KB
• Stars: 3
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Reversing_Markov_Chains

Sometimes we want to ”reverse” a Markov Chain process. Taking the inverse of the transition matrix allows this to work, but the inverse result is not a transition matrix. 

If I wanted to model a population going to work, and then going back home, negative and greater than 1 probabilities in the inverse matrix will cause issues. I propose a method to compute the ”inverse” of a transition matrix, and the result is still a transition matrix

# Applications of Process

I wanted a reverse Markov process, as I was modelling how a disease

spread through a population. I had computed probabilistic movements for

2transiting people, but the problem was that I didn’t want to compute night

and day cycles separately (it would be too much work). 

So instead, I wanted to find a method to reverse my transition matrix to account for day and night

cycles. Inverse couldn’t work, as I needed real probabilities. So, I decided

to make a new method.

This process can be used to do less work when modelling Markov systems.

If you want to model mass gatherings, and then they had to go back home

after some event, you can reverse the processes easily using this technique.

Likewise, if you wanted to somehow find what a reversed system or

”inversed” Markov process would look like, you can use this method to go

”backwards” in time.