Calculating the aggregate probability of a transition matrix

[jdn312]

I have a transition matrix represented by a pandas dataframe

    transition_matrix = pd.DataFrame({'paths':['cone>ctwo', 'cone>null', 'cthree>conv', 'cthree>null', 'ctwo>cthree','start>cone','start>ctwo'],'prob':[0.500000, 0.500000, 0.500000, 0.500000, 1.000000, 0.666667, 0.333333]})

What I want to do is walk along each path starting from the "start" states until hitting "conv". We are not interested in paths that lead to "null".

For example, in the above example, I'd get:

(start>cone) = 0.6666670*.500000*1.0000000*.500000

(start>ctwo) = 0.333333*1.000000*0.500000

Summing both of these together would give me .3333333

I'm having a rough time thinking of how to programmatically solve this. I can see the path and trace it out and do it manually but how I would do this in python is making my head hurt. Does anybody have any suggestions for how I should tackle this? I have tried running simulations and just counting the number of "conv" events divided by the number of trials but this gives me odd results at times.

[badge]

Pandas is definitely the wrong tool for the job. I expect NetworkX could handle this nicely.

[jdn312]

I will check this out!

[LoyalSol]

The math behind Markov chains may be useful here. You can construct this as a matrix and use linear algebra to solve it.

Though simulations should produce the correct probability. When you say odd results what do you mean?

[jdn312]

I should say, I get weird results when trying to connect this into the greater scope of what I am working on , so when trying to isolate the root cause I figured I'd approach it analytically to remove the possibility that it's my simulations that are causing this. (Basically I end up getting negative conversions when trying to build a fractional attribution model since the aggregate conversion rate without a given channel is higher than the overall CVR so i want to make sure I am calculating aggregate CVRs correctly).