Research Of Method To Estimate Markov State Transition Probability Matrix

Forecasting has been a work of human attention, but it has lost her mystique with thedevelopment of human society and science and technology. Markov Prediction as a quantitativemethod, having "no designation of efficiency", to historical data requires less advantages, attractedthe attention of many scholars at home and abroad. Markov Prediction is used widely in economicmanagement, education, health, natural disaster prevention and control and other areas, which arebased on initial probability of events of different State and the transition probability between statesto determine the future status, which is also a Markov model for forecasting the main ideas. Thus,it’s the key that estimate the Markova Transition Matrix before use the Markov Prediction.First of all, this paper researches the related theories of Markov prediction model andcompared and analyzed all kinds of methods that estimate the transition probability based onsummarize the researched statue at home and abroad. Then the new methods to estimate MarkovaTransition Matrix was given, which are the main contents and innovations. At last, the newmethods were applied two typical examples for making sure the extent of application of the newmethods.(1) The first part proposed the paper research goal and the significance, the analysissummarize the Markov forecast model research present situation at home and abroad, elaboratedthe Markov forecast model in some concrete question application, finally proposed this paperstudies primary coverage and research technical route.(2) The second part summarizes the theory of Markov forecasting model, describes thedefinitions and properties of Markov chain, gives the forms and traditions of State transferprobability matrix calculation, ergodicity and stationarity of the Markov chain that are detailed.The Markov forecasting model was given based on this theory.(3) The third part summarizes on the three methods for solving Markov state transitionprobability matrix, including the application of statistical methods, linear equations and quadraticprogramming method.(4) The fourth part, two new methods to solve Markov transition probabilities were given.The objective function of the first model is minimize the sum of absolute error, constraintconditions are one state that a difference between the phase error is zero, probability of a state toanother state and is equal to1, and state transition probability greater than zero. Because thesolution of the linear programming model has not only matured software and have access to analytical solutions. Therefore, convert a model into a linear programming model. The secondmodel is based on relative error and the smallest for the objective function. Constructs a target therelative error and the smallest, with a State that a phase difference between the relative error iszero, probability of a State to another State and state transition probability greater than zero andequal to1, for the constraint optimization model. Turn it into a linear model.