Re: [scilab-Users] markov state sequence with grand()‏

[诚 甄]

Hello vinsz,

Thank you very much for taking time to help me.
Yes, you are correct. I see how the function works now.
The first state in the generated sequence is not the one indicated by the parameter but rather the next one in the chain starting from that initial state.

All very clear now. Thank you again.

Dan


______________________________


On 15/04/2010 16:45, 诚 甄 wrote:

  Hello
fellow Scilab Users,

  

I am using the grand() function to generate a state sequence for a
2-state Markov chain.

It works fine to generate the sequence, but I don't quite understand
how the initial state parameter 'x0' works. Here is the code I use:

  

//-------------------

  N=50;                       //length of sequence

  P=[0.6 0.4;0.1 0.9];        //state transition matrix

  q=grand(N,'markov',P,[1]);  //initial state is '1'

  q=-(q*2.0-3.0);             //normalize to -1:+1 range

  

clf();

  plot2d3([1:N],[q],[0],rect=[0,-1.5,N,1.5],leg='2-state
Markov chain');

//------------------

  

If you run this piece of code a few times, sometimes it will start with
state '1', but not always.

  

From the help page I understand that:

  

- if I want the chain to start in state '1', then I just have to make
'x0 = [1]', as in the code above;

  

- if I want the state sequence to start from state '2', then I should
do 'x0=[2]'.

  

- if I want to get paths starting from both states I would make x0=[1
2], and each column of q (the output) would represent a path starting
at the corresponding state.

  

However, if I make x0=[1] or x0=[2], I get realizations starting from
any of the states (sometimes state 1 and sometimes state 2) and that
does not make much sense to me, because then, what are the
limiting-state probabilities that the function is using to choose the
initial state?

According to what is explained in the grand() help page, if I make, for
example, x0=[1], shouldn't the sequence 'always' start in state 1?

  

I appreciate any help and clarifications on the behaviour of this
function.

  


Hi Dan,



I think the initial state is not reported in the grand() output. You
therefore see the other state according to your transition matrix. For
instance:



N = 10000

b = zeros(N, 1) ;

for i=1:N

  b(i) = grand(1,'markov',P,[1]);

end

ii = find(b==2);



size(ii,'*')/N

 ans  =

 

 0.4095 



This is close enough to the probability to go from state 1 to state 2
being in state 1.



Hope it helps,





 		 	   		  
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