Formulation of parameter upperbound

[hyunjimoon]

During optimization, how should I formulate one parameter acting as the upper bound for other parameter?
Upper bound of effort on task to filling form frac is TF / (TF + 1) where TR is Time for Filling Forms to Task Frac. e.g. filling form takes .25 effort (measured in time) compared to the actual task. Then With p := \frac{EF}{ET} effort on filling form (EF) over effort on task (ET), p=0 means zero filling form and p = .25/(.25 + 1) = .2 means filling form for every task. (.2 when optimizing when time ratio is 1/4)

[hyunjimoon]

Could be selling point of stanify: https://mc-stan.org/docs/reference-manual/logit-transform-jacobian.html

[hyunjimoon]

If x = Time for Filling Forms to Task Frac and if we are estimating it, Stan supports the following

parameters {
  real <lower=0> x;
  real<upper = x/(1+x)> p;
}