Question

True or false: The Markov Analysis is a type of analysis that allows us to predict the future by using the state probabilities and a Matrix of Transition Probabilities.

Answer 1

Ans.

True.

Explanation:Markov Analysis is a method used to forecast/Predict the value of a variable whose future value is influenced only by its current position or state, not by any prior activity that led the variable to its current position or state and matrix of Transition Probabilities. In essence, it forecasts the activity of a random variable based solely upon the current circumstances surrounding the random variable.

ex.Steady state of the weather

In this example, predictions for the weather on more distant days are increasingly inaccurate and tend towards a steady state vector.^[2] This vector represents the probabilities of sunny and rainy weather on all days, and is independent of the initial weather.^[2]

The steady state vector is defined as:

  

but converges to a strictly positive vector only if P is a regular transition matrix (that is, there is at least one P with all non-zero entries).

Since the q is independent from initial conditions, it must be unchanged when transformed by P. This makes it an eigen-vector (with eigenvalue 1), and means it can be derived from P. For the weather example:

and since they are a probability vector we know that

Solving this pair of simultaneous equations gives the steady state distribution:

In conclusion, in the long term, about 83.3% of days are sunny.