First order Markov chains

Any help would be much appreciated! What I am trying to do is produce a program that involves Markov chains. I have a vector B which contains a random sequence of numbers from 1 to 16 in the first column (corresponding to groups types) and then in the second column of vector B which contains a quantity in the group.

What I want to do is produce a transition matrix so it gives the probability of one state going to another. Take the simple example of:

B(10,1)= [ 1; 1; 3; 3; 2; 2; 3; 1; 2; 3]

B(10,2)= [1; 3; 5; 3; 2; 6; 7; 9 ;8; 6]

Only taking the 1st column into account:

So the transition of going from a 1=>1 is 1/10

So the transition of going from a 1=>2 is 1/10

So the transition of going from a 1=>3 is 1/10

So the transition of going from a 2=>1 is 0/10

So the transition of going from a 2=>2 is 1/10

So the transition of going from a 2=>3 is 2/10

So the transition of going from a 3=>1 is 1/10

So the transition of going from a 3=>2 is 1/10

So the transition of going from a 3=>3 is 1/10

The transition matrix would be output into a 3x3 matrix would be:

Trans=[0.1, 0.1, 0.1; 0.0, 0.2, 0.1; 0.1, 0.1, 0.1]

Any help would be great!

Answer 1

[Youssef Khmou]

hi olig,

You can try to use the function "HMMESTIMATE" which a default Matlab function :

As an example, we take a sequence of numbers from 1 to 10:

 seq=1:10;

The states is a matrix B with the same length as seq :

 B=round(10*rand(10));

The function generates the transition and emission matrices as the following :

 [Trans,Emis]=hmmestimate(seq,B)

I think this example can be adjusted to your case .