Modeling observed data that can take values between 0 &1

Questions
1

Hi all,
How do we write the likelihood function for an observed variable that can only take values between 0-1 and is continuous. I am trying to do a measurement error model in which one of the input variables is a proportion and has a standard error associated with it. As such it can only take values between 0-1 but the standard error on the quantity may put it out of that range. Any reference would be highly appreciated.
Thanks.

2

Depending on the details, either pm.Uniform or pm.Beta seems like it would work.

3

Thanks for answering. In general how do we constrain the likelihood to be between a given range?

4

For uniform and beta priors this is guaranteed. For others, you can use pm.Bound() to force it between a lower and upper bound and have the machinery take care of normalization.