Markov Chain Inputs
A Markov chain is a method that helps you determine the sequence of events that will result from different inputs. A Markov chain can be used to capture sequences of events without having to worry about the uncertainty of what will happen next or making choices based on prior information.
As a simple model, there are two variables: the inputs (actual events) and the outputs (predictions). The outputs depend on how the inputs are used.
Suppose you use an input of “We have just won a soccer game.” How should you use this event? The output would be: What is our predicted score after the game? While “We have just won a soccer game” is an interesting input to use, it does not help much in the prediction process.
If you use “We have just won a soccer game” as your input, you should “evaluate” that using “What is our predicted score after the game?” Should you compare the predicted score to the actual score?
This final input gives you the most “input information”. This information lets you work with the equations. For example, if we had a situation where “We have just won a soccer game” was our input and we predicted a score of 10-0, then the final output would be: What is our predicted score after the game?
In order to find out which equations are best for prediction, you need to evaluate their accuracy. In order to do this, you want to know if the outputs would have been different if we had used different input events. What would have happened if we had given the data a different meaning?
To find out this, you need to evaluate each set of test cases by taking the difference between the actual and predicted results. These results need to be useful and measurable. Testing may be performed by using an objective function that measures the deviation of the predicted results from the actual ones.
Evaluating the tests and finding out that do well will help you find which models are most useful. This information can be used in future predictive models. It can also help you refine the model and therefore improve the predictions.
However, there is a problem with assigning a Markov chain to a single input. If there are many inputs to test, you will have a difficult time testing each Markov chain.
You can use a random walk to test each Markov chain. However, there are a number of other approaches.
One approach is to combine more than one SPSS Help Online to make a Monte Carlo simulation. This simulation will allow you to run each Markov chain several times to see if they provide useful results.
Another approach is to test each Markov chain in isolation and in separate test cases. Each Markov chain will be run separately in a separate set of test cases.