https://github.com/rtmigo/markov_walk_py
🔢 Python module that calculates probabilities for a random walk in 1-dimensional discrete state space
https://github.com/rtmigo/markov_walk_py
absorbing-markov-chains absorbing-states markov-chain mathematics numpy probability probability-theory random-walk stochastic-matrix stochastic-models
Last synced: about 2 months ago
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🔢 Python module that calculates probabilities for a random walk in 1-dimensional discrete state space
- Host: GitHub
- URL: https://github.com/rtmigo/markov_walk_py
- Owner: rtmigo
- License: bsd-3-clause
- Created: 2021-03-07T20:56:42.000Z (about 4 years ago)
- Default Branch: master
- Last Pushed: 2022-05-06T20:12:19.000Z (almost 3 years ago)
- Last Synced: 2025-01-21T15:32:17.778Z (3 months ago)
- Topics: absorbing-markov-chains, absorbing-states, markov-chain, mathematics, numpy, probability, probability-theory, random-walk, stochastic-matrix, stochastic-models
- Language: Python
- Homepage:
- Size: 29.3 KB
- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
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README
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# [markov walk](https://github.com/rtmigo/markov_walk#readme)
This module solves a particular mathematical problem related to probability theory.
-----
Let's say a completely drunk passenger, while on a train, is trying to find his car. The cars are
connected, so he wanders between them. Some transitions between cars attract him more, and some
less.
At the very beginning and at the very end of the train there are ticket collectors: if they meet a
drunkard, they will kick him out of the train.[*](#note1)
We know which car the drunkard is in now. The questions are:
- What is the likelihood that he will be thrown out by the ticket collector standing at the
beginning of the train, and not at the end?
- What is the likelihood that he will at least visit his car before being kicked out?
# On a sober head
We are dealing with a discrete 1D random walk. At each state, we have different probabilities of
making step to the left or to the right.
| States | L | 0 | < 1 > | 2 | 3 | 4 | 5 | R |
|---------------|-------|-------|---------|-------|-------|-------|-------|-------|
| P(move right) | ... |**0.3**| 0.5 |**0.7**| 0.4 | 0.8 | 0.9 | ... |
| P(move left) | ... | 0.7 | 0.5 | 0.3 | 0.6 | 0.2 | 0.1 | ... |
The probability to get from state `1` to state `2` is `0.7`.
The probability to get from state `1` to state `0` is `0.3`.
Suppose the motion begins at state `1`. What is the exact probability that we will get to state `R`
before we get to state `L`? What is the probability we will get to state `3` before `L` and `R`?
# What the module does
It uses [Absorbing Markov chains](https://en.wikipedia.org/wiki/Absorbing_Markov_chain) to solve the
problem. It performs all matrix calculations in `numpy` and returns the answers as `float` numbers.
# How to install
```bash
cd /abc/your_project
# clone the module to /abc/your_project/markov_walk
svn export https://github.com/rtmigo/markov_walk/trunk/markov_walk markov_walk
# install dependencies
pip3 install numpy
```
Now you can `import markov_walk` from `/abc/your_project/your_module.py`
# How to use
```python3
from markov_walk import MarkovWalk
step_right_probs = [0.3, 0.5, 0.7, 0.4, 0.8, 0.9]
walk = MarkovWalk(step_right_probs)
# the motion begins at state 2.
# How can we calculate the probability that we will get to state R before we get to state L?
print(walk.right_edge_probs[2])
# the motion begins at state 1.
# What is the probability we will get to state 3 before L and R?
print(walk.ever_reach_probs[1][3])
```
- `walk.ever_reach_probs[start_state][end_state]` is the probability, that after infinite wandering
started at `start_state` we will ever reach the point `end_state`
- `walk.right_edge_probs[state]` is the probability for a starting `state`, that after infinite
wandering we will leave the table on the right, and not on the left
By states we mean `int` indexes in `step_right_probs`.
-----
* Perhaps you are worried about why the ticket collectors are going to kick the
passenger out. The reason is that he is traveling on a lottery ticket.