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I am building a model that simulates the travel patterns of electric cars using a series of iterative conditional distributions. I have a dataset to build the pdfs.

In one part of the model I generate a parking time from a conditional distribution.

I create a parking time distribution for example given the time of day and location etc.

I am using a Bayeisan approach because given certain condition sometimes no observations may be returned from the dataset because none were recorded so no distribution can be created and the simulation stops

So first of all I assume a uniform Prior distribution.

https://dl.dropbox.com/u/54057365/All/prior.JPG [Broken]

Secondly I return the data in the database given the conditions and create the likelihood function.

https://dl.dropbox.com/u/54057365/All/likelihood.JPG [Broken]

Then I combine the prior distribution and posterior distribution to form the posterior distribution and I generate a value.

https://dl.dropbox.com/u/54057365/All/posterior.JPG [Broken]

My question is as follows, whenever no observations are returned the likelihoods is 0 so the posterior distribution is flat like prior distribution.

Instead of using a uniform prior I want to use an informed prior.

I have set the all the hyperparamters of the bins to 1 in the prior distribution but can I assign the hyper parameters according to some distribution instead?

How would I do this?

Thanks

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# Bayesian probability question

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