A 2 state Markov model creates a value of 1 when it is in state 1 and a value of

Question

A 2 state Markov model creates a value of 1 when it is in state 1 and a value of 2 when it is in state 2. Possible combinations of transition probabilities are shown below.

A 2 state Markov model creates a value of 1 when it is in state 1 and a value of 2 when it is in state 2. Possible combinations of transition probabilities are shown below. al 1-0. al 2-0.9 a 21-09 a22-0.1 al 1-05 12-05 a 21-09 2-0,1 all -0.1 a12 0.9 0.5 a22 -0.5 all 0.9 12-0.1 a2, -0.9 a22 0.1 all 0.95 a12 0.05 a21 0.05 a22 0.95 all 0.5 a12-05 21- 0.5 a22-05 Using the 3 sets of observations below, pair the most likely set of transition probabilities from rows 1-6 above. MODEL MODEL MODEL

Explanation / Answer

1) In the first chart we see that the probability of transition into the same state, be it state 1 or state 2 is very low as we see that the there are transitions happening almost at east step.

Therefore, he row of probabilities out of the 6 which ould be the used model for this graph would be: the first one that is:

a11 = a22 = 0.1 and a21 = a12 = 0.9

2) Here in the second chart it looks as if there is an equal probability of having a transition to the same state or a different state as we see from the chart that in half of them , transition happened in the same state and in rest to a different state. Therefore this chart can be represented by the set of probabilities that are in the 6th row.

a11 = a22 = a21 = a12 = 0.5

3) In the third chart, we see that there is a very high transition probability from the second state to the first state and very low transition probability from state 1 to state 2 as it remains in state 1 for a long time. therefore the set of probabilities which match the situation here would be: the 4th row transition probabilities: that is:

a11 = a21 = 0.9 and a22 = a12 = 0.1

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