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title: "Informed prior"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575376/Informed%20prior"
format: markdown
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An informed prior has a distribution that adds information to the Bayesian inference. It is either the result of a previous statistical analysis of other data that gave you information about the parameter ([example](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575649)), or it has been constructed from an expert's estimate of the parameter.

 

Informed priors can be modeled in various ways. A [conjugate prior](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575373) will be an informed prior if the parameter values create a distribution with a shape that is different from an uninformed prior. For example, a Beta(1,1,1) distribution is usually considered an [uninformed prior](https://modelassist.epixanalytics.com/space/EA/26575372/Uninformed+priors) when [estimating a binomial probability](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574975) because it assigns equal weight to all values of p between 0 and 1. Thus, a Beta(4,2,1) distribution, for example, is an informed prior because its shape is different: it peaks at 0.75, as shown in the figure below:

 

![image](media://cf92a7b0-e286-49f3-b4e2-ff726f662eb0)

 

 

Informed priors can be constructed graphically to describe an [expert's estimate](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575374), but it is a good idea to check whether there are data underlying the opinion that could be used in a statistical analysis.

 

An informed prior can also come out of a logical argument. For example, if 100 people are in a room, we might estimate the number of people who are female to be Binomial(0.5,100) before collecting any information about the group ([example](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575397)).

 

 

 

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