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(4)

The *shape* of the prior distribution embodies the amount of knowledge we have about the parameter to start with. The more informed we are, the more focused the prior distribution will be:

** Example 1**: Comparison of the shapes of relatively more and less informed priors

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The *shape* of the likelihood function embodies the amount of *information* contained in the data. If the information it contains is small, the likelihood function will be broadly distributed, whereas if the information it contains is large, the likelihood function will be tightly focused around some particular value of the parameter:

** Example 2**: Comparison of the shapes of likelihood functions for two data sets. The data set with the greatest information has a much greater focus.

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** Example 3**: The likelihood is flat relative to the prior so has little effect on the level of knowledge (the prior and posterior are very similar)

** Example 4**: The likelihood is highly peaked relative to the prior so has a great influence on the level of knowledge (the likelihood and posterior have very similar shapes)

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On the other hand, if the focus of the likelihood function is very different from the prior we will have learned a lot from the data:

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** Example 6**: The likelihood is highly peaked relative to the prior so has a great influence on the level of knowledge (the likelihood and posterior have very similar shapes)

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** Example 7**: The likelihood is highly peaked relative to the prior and focused on one extreme of the prior's range, so is in reasonable disagreement with the prior, yet the posterior is strongly focused despite the disagreement because the parameter cannot be negative and is therefore constrained at zero.