# Prior Truncation in brms [lb,ub]

Hi there,

Is there an inconsistency or limited application in the brms model priors and other functions??

When defining priors, it is technically allowed to truncate the priors of a model parameter class, e.g. like this

``````prior <- c(prior(student_t(1, 0, 1), class = b, lb=-4, ub=4))
``````

but also to specify priors for single coefficients in a model:

``````prior <- c(prior(student_t(1, 0, 1), class = b, coef=IndepVariable))
``````

What is not allowed (as indicated by an error message) is this:

``````prior <- c(prior(student_t(1, 0, 1.5), class = b, coef=IndepVariable, lb=-4, ub=4))
``````

Why?
Or maybe I should ask: Is it possible to change this in future versions? :)

Here are some reasons for why I think this needs to be possible:

1. Defining the priors for every parameter properly seems to be a prerequisite of some other functions like hypothesis() or nlf(). And it seems to me, that some hypotheses tests (e.g. hypothesis(model, “IndepVariable==0”) cannot be done with truncated priors because of the coding restriction.

2. in logistic models it is, in some cases, almost meaningless to have samples smaller than -5 or larger than 5 because they are parameters on a log scale. This might be moreover parameter specific in more complex models (e.g. a large +intercept basically excludes large additional effects like +5 on a log-scale).

3. Negative values of some -specific- parameters in regressions are a priori meaningless (e.g. of ‘growth rate’ ), but still normally distributed (that is, one can not use gamma distributions), and currently it seems not possible to specify such a priori assumptions without willingly miss-specifying the model.

I currently run a model with such priors, just to see what happens…

``````prior <- c(prior(student_t(1, 0, 1.5), class = b, lb=-4, ub=4),
prior(student_t(1, 0, 1.5), class = b, coef=IndepVariable))
``````

Intuitively I guess this will not lead to a truncated prior for IndepVariable

Best, René

That’s because brms defines regression coefficients as a single vector, which can only have a common lower and upper boundary (if I am not mistaken). Splitting up these vectors in brms automatically would be a tone of programming work that I don’t want to invest since there is an easy workaround using brms’ non-linear syntax.

``````bform <- bf(
y ~ a + b, nl = TRUE,
lf(a ~ <other predictors>, center = TRUE),
lf(b ~ 0 + IndepVariable, cmc = FALSE)
)
``````

Hi Paul,

thank you very much for your reply. It’s great that there is a workaround, but I regret to say, I do not understand it. :) Mostly because, I do not know (where to look at) how this formula-definition relates to a prior definition, or to the implication that some priors are acceptable in brm while others are not, depending on the bf formula I define. (This also seems not to be the right thinking of me because I can use the prior() function (giving me the mentioned error message) without even defining a model.

Edit:
Ah… no wait… I got it :)
so my part in this solution would be connecting the above model to the ‘dpar’ prior, right?
(This was not too obvious, never having seen the lf() before ;))

`````` prior(student(1, 0,1), dpar = IndepVariable, lb = -4, ub = 4))
``````

Best, René

See `https://discourse.mc-stan.org/t/horseshoe-prior-on-subset-of-predictors/8140/8` for a similar problem and corresponding solution.

Thanks again. :) Are there any issues in defining nlpar priors in lf() functions one should know?
Otherwise, I guess this is solved. Thank you.

Not that I am aware of.

Just for the record:
A prior definition (“normal” brm model) like this:

`````` c(prior(student_t(1, 3, 1.5), class = b, lb=0,ub=5),
prior(student_t(1, 0, 1), class = b, coef=IndepVariable))
``````

Actually yields a zero-truncated positive prior for IndepVariable with mean=0 (according to prior_samples() ). Have no idea how or why it works this way, but it works :). In other words, the general truncation for class=b is taken over to other more specific priors such as the coef-prior below, without taking overwriting the distribution for the coef-prior.
So this seems nice for cases in which there are no other relevant priors that would be cut-off this way, … and the above definition would give the same prior for IndepVariable as:

``````prior(student_t(1, 0, 1), class = b, coef=IndepVariable, lb=0, ub=5)
``````

If it was allowed to define it this way.

Best, René