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Gagan
October 11th 2010, 04:55 PM
I have a question related to modeling with Bayesian Statistics and I was wondering if you smart folks on here can help me out.

I was just wondering how one would go about modelling walking times using Bayesian. For ex. I walk to school 5 days a week, yielding walking times t1, t2, t3,......,t21 for the month of september 2010 (excluding labour day).

What's one way one could potentially model these walking times (with prior and posterior distributions).I know the distbn of parameters is important for bayesian making this more challenging but what could one do in this case, as well as the assumptions one would make

I saw a question similar to this in one of the guides for Exam C (not really an exam question though) so I was just curious if someone could help me out.

I was thinking walking times could be exponential, but I'm not sure what would a sensible prior be for ex. that would make the model good. Of course I'm sure there are many different ways this can be done but how would you guys do it?

thanks
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alekhine4149
October 11th 2010, 05:23 PM
Haha I like the way you think. Okay, I find this problem to be a frustrating dilemma already because I'm torn between tools from my limited belt. I am leaning toward Normal/Normal conjugate pair, and my reasons are as follows:

I want a conjugate pair to allow ease and frequency of updates. I don't like exponential model because the standard deviation is equal to the mean, and this can't be refined due to constraints of the single parameter. I don't know how you walk, but I'm almost positive it doesn't have that much variance! Normal annoys me since it allows negative values, but since your standard deviation will likely be small, those will never occur in practice.

So I'd create a hypothetical mean and standard deviation based on your best guess, and then use empirical times for updates. You need both theoretical and true values to make it work.

If I knew more conjugate pairs, I'd recommend modeling your walking time as a gamma since you can shrink the coefficient of variation. Or as a lognormal, since this disallows negative values. :geek::Smart::Devil: I'd prefer gamma since exponential is used for waiting time, and gamma is a sum of exponentials - it seems like a natural fit.

Gagan
October 11th 2010, 06:22 PM