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By Vijay Cupta

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Example text

Py. For more information see “Working with the code” on page xi. Credible intervals Once you have computed a posterior distribution, it is often useful to summarize the results with a single point estimate or an interval. For point estimates it is common to use the mean, median, or the value with maximum likelihood. For intervals we usually report two values computed so that there is a 90% chance that the unknown value falls between them (or any other probability). These values define a credible interval.

To update the distribution based on new data (the vanilla cookie), we multiply each prior by the corresponding likelihood. The likelihood of drawing a vanilla cookie from Bowl 1 is 3/4. The likelihood for Bowl 2 is 1/2. info Mult does what you would expect. It gets the probability for the given hypothesis and multiplies by the given likelihood. Normalize() The result is a distribution that contains the posterior probability for each hypothesis, which is called (wait now) the posterior distribution.

If the selections of X and Y are independent, CDF 3 5 = CDF 1 5 CDF 2 5 where CDF3 is the distribution of Z. I chose the value 5 because I think it makes the formulas easy to read, but we can generalize for any value of z: CDF 3 z = CDF 1 z CDF 2 z In the special case where we draw k values from the same distribution, CDF k z = CDF 1 z k So to find the distribution of the maximum of k values, we can enumerate the proba‐ bilities in the given Cdf and raise them to the kth power. ps] return cdf Max takes the number of selections, k, and returns a new Cdf that represents the distri‐ bution of the maximum of k selections.

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