- #36
bradyj7
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Okay, thank you for explaining that and for your help.
chiro said:Basically what you would have to do is break it up into a small number of intervals (which you have done) and then consider all the branches to get a complete set of conditional distributions.
So instead of making your conditional distribution based on a continuous variable, you make it based on a discrete one.
So in other words you restrict your parking and journey times to fit into "bins" and then you look at each conditional distribution for each of the branches.
For example if you allow the smallest time interval to be ten minutes: then you consider conditional distributions for total times in terms of lumps of these intervals.
So if you have n of these intervals, you will get 2^n branches. Some branches may have zero probabilities, but in general you will have 2^n individual branches corresponding to all the possibilities that you can take.
So an example might be P(Total Journey Time = 30 minutes| First 10 = Travel, Second 10 = Travel, Last Ten = Park) and any other attributes you need.
To count up total journeys, you basically sum up all the positive branches (i.e. when all the times you have a journey) and for parking you do the same for those.
Basically what this will look like is a dependent binomial variable, and what you do is estimate these probabilities from your sample. From this you will have a distribution for n intervals given a history of what you did and by considering whatever subset of these probabilities you wish, you can find things like the expectation.
So an example might be P(Total Journey Time = 30 minutes| First 10 = Travel, Second 10 = Travel, Last Ten = Park) and any other attributes you need.
A transition probability matrix is a mathematical tool used to represent the probabilities of moving from one state to another in a system that undergoes a series of transitions. It is commonly used in fields such as physics, chemistry, and biology.
Yes, two transition probability matrices can be combined using matrix multiplication. This involves multiplying each element in one matrix by the corresponding element in the other matrix and then summing the products. The resulting matrix will represent the combined probabilities of transitioning from one state to another.
Combining two transition probability matrices allows for the representation of more complex systems with multiple transitions. It can also be used to model the behavior of a system over time, as the combined matrix can be repeatedly multiplied by itself to represent multiple transitions.
Yes, there are some limitations to combining transition probability matrices. The matrices must have the same dimensions, and the elements in each matrix must represent probabilities (i.e. they must be between 0 and 1). Additionally, the combined matrix may not accurately represent the behavior of the system if the individual matrices are not based on the same underlying data.
Combining transition probability matrices can be applied in various real-world scenarios, such as modeling the spread of diseases, predicting stock market trends, and analyzing population dynamics. It can also be used in machine learning and artificial intelligence to model decision-making processes and predict future outcomes.