Parser Warnings for Uniform Priors

[Michael Betancourt]

Serious proposition — can we have the parser spit out warnings if
there are modeling features we don’t like? inv_gamma(small, small)
might be hard to spot given the different ways a small number can
be defined, but uniform priors are easy. Having any model where
the uniform distribution is used spit out a warning like

“You have used a uniform distribution on a bounded space which
can often lead to misbehaved models. If you encounter fitting
problems check that the parameter <name> has the bounds
(<lower>, <upper>) for example

real<lower = <lower>, upper=<upper> <name>;

But please consider replacing such hard constraints with a
soft constraint, such as

<name> ~ normal((<lower> + <upper>) / 2, (<upper> - <lower>) / 2).”

[Daniel Lee]

Is there a good reason for the uniform distribution?

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[Michael Betancourt]

It’s used almost exclusively when people want to add

hard constraints to their model (which we discourage)

and almost always do wrong (because they don’t add

the corresponding bounds on the parameters).  Almost

half of the modeling emails this week were about this

and it seems to be growing.

[Daniel Lee]

Think someone's teaching a class and suggesting this?

Maybe we need to put it up on the blog.

[Bob Carpenter]

The inv_gamma(0.001, 0.001) thing comes from the BUGS examples
which tried to use it to approximate flat priors. No idea where
the interval priors are coming from, but I assume the same desire
not to add information to the data.

The uniform() is really just there because it seemed like it
was necessary for completeness. As is, the only possible use for
it is if you need a normalized probability. Otherwise, it's
redundant with the constraint declarations. And it's definitely
bad if you have an unconstrained variable drawn according to
a uniform.

We could try to detect some of these. We have the parse tree for
the Stan program as an abstract syntax tree before we do code
generation. Or we could try to catch it as it happens.

- Bob

[Michael Betancourt]

Interval priors are coming from people who have been taught
that prior information should be encoded in hard constraints,
i.e. that you choose extreme values and then claim to be
“ignorant” within them. This unfortunately gets taught a lot
in the sciences which is why I think we’re seeing it more and
more.