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Example 7.2.1, determine the form of an exact < -prediction interval for an additional future…

Example 7.2.1, determine the form of an exact

Example 7.1.1

Suppose that we observe a sample Example 7.2.1, determine the form of an exact &lt; -prediction interval for an additional future...  from the Bernoulli(θ) distribution with Example 7.2.1, determine the form of an exact &lt; -prediction interval for an additional future... unknown. For the prior, we take π to be equal to a Beta(α,ß)     density  Then the posterior of π is proportional to the likelihood

Example 7.2.1, determine the form of an exact &lt; -prediction interval for an additional future...

This product is proportional to

Example 7.2.1, determine the form of an exact &lt; -prediction interval for an additional future... 

We recognize this as the unnormalized density of a Beta Example 7.2.1, determine the form of an exact &lt; -prediction interval for an additional future... distribution.So in this example, we did not need to compute m Example 7.2.1, determine the form of an exact &lt; -prediction interval for an additional future... to obta α = ß i.e., we have a uniform prior on θ Then the posterior of θ is given by theBeta(11, 31) distribution. We plot the posterior density in Figure 7.1.3 as well as the

prior.

 

 

 

Example 7.2.1, determine the form of an exact &lt; -prediction interval for an additional future...

The spread of the posterior distribution gives us some idea of the precision of any probability statements we make about θ . Note how much information the data have added, as reflected in the graphs of the prior and posterior densities