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Probability per weekly event (with happy hamsters)

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  • 18-11-2016 10:42pm
    #1
    Sordini
    Registered Users Posts: 50 ✭✭


    Hi all
    I had a population of 100 hamsters.
    Each week there is was a risk that their mood could change and certain rules apply (attached).
    The study is now over and I have results.
    I wish to repeated the test, using the old results to predict the weekly probabilities of a mood change.
    Weeks 1 to 17 don't matter in the experiment, accuracy there is not important. Only the result at the end. Given that, can I use this fairly simple approach or is there better way to approach this?
    All comments welcome
    S


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    #2
    Yakuza
    Registered Users Posts: 5,141 ✭✭✭Yakuza


    I would use one of the Nelson-Aalen or Kaplan-Meier estimators if I were interested in the cumulative hazard of not being happy over time.

    The KM estimator is a bit easier conceptually, you would work out the weekly hazard rate of becoming OK from Happy and from there you could work out the cumulative probability of staying happy.

    The fact there's only one transition from Ok to Sad over the entire 18 sets of observations would indicate a very low overall probability of this happening at all.

    I am assuming that it's also not possible to become Happy from the OK state, so the transition diagram is fairly simple Happy--->Ok--->Sad.

    Is that real data? Your spreadsheet would suggest you're trying to model values based on an assumed probability. As a side note, the probabilities of moving from Happy to OK and OK to sad don't necessarily add to 1 - to model your situation fully you'd need a matrix with nine values (probabilities of moving from all possible states to all possible states (3*3) - some entries will be zero)

    If you really only care about the end result (then why store all the interim values?) then you could state the the approximate probabilities of remaining happy, becoming OK or becoming sad after 18 weeks are 77/101, 23/101 and 1/101.


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    #3
    Sordini
    Registered Users Posts: 50 ✭✭Sordini


    Dear Yakuza! Thank you so much for those two links. I will for sure take a good look at that KM one.
    Yes you are correct. It is not possible to go 'up' in happiness at all.
    The data is not real. In essence it is random or more accurately it will be simulated. Specifically poison distribution in simulation software.
    And yes you are also correct: I only care about the end result or range of simulated results. So storing weekly data is not essential. My goal is ultimately to make sure my inputs of 0.985 & 0.015 per event are fit for purpose and will bring me to the desired numbers. The simulation objective is to extract the min, median and max.


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