Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find the probability of a state at a given time in a Markov chain - Set 1 in Python
Suppose we have a Markov chain graph g; we have the find the probability to reach the state F at time T if we start from state S when time t = 0. As we know a Markov chain is a random process consisting of various states and the probabilities to move one state to another. This can be represented as a directed graph; the nodes are states and the edges have the probability of going from one node to another. From one state to another, it takes unit time to move. The sum of the probabilities of the outgoing edges is one for every node.
So, if the input is like N = 6, S = 4, F = 2, T = 100, then the output will be 0.28499144801478526
To solve this, we will follow these steps −
table := a matrix of size (N+1)x(T+1) and fill with 0.0
table[S, 0] := 1.0
for i in range 1 to T, do
for j in range 1 to N, do
for each k in G[j], do
table[j, i] := table[j, i] + k[1] * table[k[0], i - 1]
return table[F, T]
Example
Let us see the following implementation to get better understanding −
def get_probability(G, N, F, S, T): table = [[0.0 for j in range(T+1)] for i in range(N+1)] table[S][0] = 1.0 for i in range(1, T+1): for j in range(1, N +1): for k in G[j]: table[j][i] += k[1] * table[k[0]][i - 1] return table[F][T]; graph = [] graph.append([]) graph.append([(2, 0.09)]) graph.append([(1, 0.23),(6, 0.62)]) graph.append([(2, 0.06)]) graph.append([(1, 0.77),(3, 0.63)]) graph.append([(4, 0.65),(6, 0.38)]) graph.append([(2, 0.85),(3, 0.37), (4, 0.35), (5, 1.0)]) N = 6 S, F, T = 4, 2, 100 print(get_probability(graph, N, F, S, T))
Input
6, 4, 2, 100
Output
0.28499144801478526
241 Views
