Markov Chains: How much steps to conclude a Transition Matrix

3

I have just learned Markov Chains which I am using to model a real world problem. The model comprises 3 states [a b c]. For now I am collection data and calculating transitional probabilities:-

T[a][b] = #transitions from a to b / #total transitions to a

However I am stuck at determining the correct Transition Matrix. As I am getting more data, the matrix is changing drastically. So when do I finalize Transition Matrix? Does that mean that my data is too random and cannot be modelled or I am doing some mistake here?

Mangat Rai Modi

Posted 2015-07-17T21:04:15.433

Reputation: 509

Answers

3

I expect you have, or can make, a matrix of transition counts. Consider the data in each row to be draws from a multinomial distribution. Then you should be able to use sample size calculations for the multinomial to get off the ground.

It is also possible that your data is not well described by a simple Markov chain. There are some available techniques for this, e.g. multistate modelling, but which may or may not fit your particular problem.

conjectures

Posted 2015-07-17T21:04:15.433

Reputation: 321