Question
how can i apply markovian analysis in problem solving given a table of raw statistical data
Answer
<P>Hello Mogbolu,<BR><BR>Is your name Nigerian? It doesn't matter -- it's just if you look at some of my other posts to this forum, you will see that I have an interest in linguistics as well as science. <BR><BR>Your question seems a bit advanced for high school. I did not study Markov until college. However I do remember studying matrices so if you have done that you can handle Markov. <BR><BR>I am in the forest inventory business, so I'll use that as an example. However if you can follow the math you can use the same method for a variety of statistical analysis.<BR><BR>Suppose your landscape is 60% forest and 40% nonforest. Over a certain time period (say a 5-year inventory), you expect 80% of your forest to remain forest and 20% to revert to nonforest. You also expect 90% of your nonforest to remain nonforest and 10% to actually revert back to forest.<BR><BR>So your expected distribution in the next cycle is:<BR><BR>0.8 0.1 x 0.6 = 0.52<BR>0.2 0.9 0.4 0.48<BR><BR>So after 5 years you would expect your landscape to be 52% forest and 48% nonforest.<BR><BR>If you can expect trends to stay constant over the next 10 years then you would just multiply by your matrix again.<BR><BR>0.8 0.1 x 0.52 = 0.464<BR>0.2 0.9 0.48 = 0.536<BR><BR>After 10 years you would expect 46.4% forest and 53.6% nonforest.<BR>As long as you expect trend to stay constant, you can continue multiplying by the Markov matrix. <BR><BR>The good news is, that over time, you can expect the process to stabilize. In this case, the process will stabilize at 1/3 forest and 2/3 nonforest.<BR><BR>Put (1/3,2/3) in the prior, multiply by the Markov matrix, and you get (1/3,2/3) for the posterior distribution.<BR><BR>Hope this helps,<BR><BR>Joe M.<BR>Forest Inventory and Analysis<BR>Knoxville, TN <BR><BR><BR><BR></P>
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