Markov Analysis Assignment Help Australia

Markov Analysis Assignment Help

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What Is Markov Analysis Process?

There are different phenomena, many of them in the social field, which present a temporal evolution such that they can be modelled according to a Markov analysis process.

A Markov process is a series of experiments in which each one has m possible outcomes, E1, E2..... Em, and the probability of each outcome depends exclusively on the one obtained in the previous experiments.

For example: if there are three brands of detergents on the market, each of which has a certain portion of that market in week 1, the following week the distribution may change depending on consumer decisions (continue with the same brand or change for another), and this decision depends a lot on the last purchase. Many other situations present this pattern of behaviour: the values of the shares of the stock market day by day, the distribution of the population between different regions from year to year, etc.

Mathematically, a Markov analysis process is modelled by a transition matrix.

This is nothing more than a probability matrix, where each element 'pij' represents the conditional probability that the system passes from a current state 'i' to the next state 'j'.

Traditional mathematical solving is tedious since if you want to see the evolution over a certain period, it will be necessary to repeat matrix operations as many times as you want to analyze.

A resolution has been applied using the possibilities offered by system dynamics, which also allows better visualization of the phenomenon, and includes other additional elements to the phenomenon under study.

Applications of Markov Analysis Process

A hypothetical process {X (t): t∈ [0, T]} is a set of arbitrary variables defined for each t∈T of a time interval [0, T]. This comes to tell us that when a given instant of time t is fixed, what happens at that time, follows a random behaviour, given from a function ft (x), where x denotes the occurrence value of the phenomenon to be studied. An important family of stochastic processes is formed by the so-called Markova processes. The following property is verified in them:

P (Xn+1=j|Xn=i, Xn−1=in1"¦ X0=i0) =P (Xn+1=j|Xn=i) =pij (n+1) ∀n∈N

In other words, the possibility of an event taking place, based on the previous events, depends exclusively on the probability of the previous event. A very important family within the Markova processes are the so-called homogeneous Markova processes in which pij (n + 1) is constant for all n ∈N. The applications of Markov processes to different areas of knowledge are diverse: weather forecasting, classification of healthy or sick patients, or even in the cyber world, in Google web page search engines for example. To illustrate the use of the Markov process in the modelling of various sports problems.

Problem 1: Suppose we want to study the sporting results of a given Soccer team from the professional league, let's put it in the Premier League. To do this we explain the random variable X = 'Win i games in a row' where in this example it takes a finite number of values i∈ {−2, −1, 0, 1, 2}. To know the future behaviour of this mathematical model and in this way, to be able to predict the number of games that a team is going to win at the end of the season, we must define a transition matrix P, which establishes the probabilities between the different scenarios, consider for example P =

row i indicates the state 'win i games in a row', while column j, the state 'win j games in a row', while the element (i, j) of the matrix denotes the probability of occurrence of passing the state i to state j, for instance, the probability of not winning any game knowing that we have lost two is 0.1, which corresponds to element (1, 3) of the matrix.

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