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Re: simulating a 2-state Markov process

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41417] Re: [mg41369] simulating a 2-state Markov process
  • From: Bobby Treat <drmajorbob at mailblocks.com>
  • Date: Sun, 18 May 2003 05:04:28 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Oh yeah, I didn't show you how to simulate draws.

For example:

sim[H] := If[Random[] < p, T, H]
sim[T] := If[Random[] < q, H, T]
p = .45; q = 0.35;
NestList[sim, H, 30]

Bobby

-----Original Message-----
From: David E. Burmaster <deb at alceon.com>
To: mathgroup at smc.vnet.net
Subject: [mg41417] [mg41369] simulating a 2-state Markov process

Dear MathGroup,

Can someone please suggest an efficient way to use Mathematica to
draw realizations from a 2-state Markov process as outlined below?

i want to specify the transition probabilities and the number of
transitions to simulate.

=-=

for notation....

1. let's denote the two states as H and T (for Heads and Tails, even
though i am thinking about a process more general than flipping a
coin)

2. let's denote the four conditional transition probabilities as follows

    prob(T | H) = p

    prob(H | H) = 1-p

and

    prob(H | T) = q

    prob(T | T) = 1-q

3. for initial conditions, let the process begin in state H

=-=

within this framework, p and q can take any values in the unit square

	(0, 1] x (0, 1]


=-=-=

thank you for your help
dave



--
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David E. Burmaster, Ph.D.
Alceon Corporation
POBox 382069
Cambridge, MA 02238-2069

617-864-4300

deb at alceon.com
www.alceon.com

************************************


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