Bayesian (continuous) logistic regression model with Beta likelihood? I have a problem where my target variable are continuous/float values in the range [0,1]. If my data were integers in {0,1} this would be a simple logistic regression / Bernoulli likelihood problem. But because my target variable are not integers, I believe that a Beta likelihood would be more appropriate.
I come from a primarily Bayesian background, so setting up a Beta likelihood in PyMC3 or Stan should be trivial. But I want to clarify if this is a sensible approach, something that's been done before, or if there is a reason that analysts don't do this.
Similarly, as my Beta likelihood model is to logistic regression, I hypothesize that a Dirichlet likelihood model would be to multi-class logistic regression. Is this sensible?

Yes, with continuous target you would be using beta regression and Dirichlet regression for multi-“class” problems. Usually it would be reasonable to re-parametrize the beta distribution into using mean and precision.
