# Efficient code to sum two dependent random variables

**URL:** <https://discourse.mc-stan.org/t/efficient-code-to-sum-two-dependent-random-variables/31967>\
**Category:** Modeling\
**Tags:** techniques\
**Created:** [July 4, 2023, 9:06am UTC](https://discourse.mc-stan.org/t/efficient-code-to-sum-two-dependent-random-variables/31967 "2023-07-04T09:06:43Z")\
**Posts on this page:** 1\
**Showing post:** 14

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**Author:** ![twistedVine](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/twistedvine/32/18073_2.png) [@twistedVine](https://discourse.mc-stan.org/u/twistedVine)\
**Post date:** [July 18, 2023, 12:59am UTC](https://discourse.mc-stan.org/t/efficient-code-to-sum-two-dependent-random-variables/31967/14 "2023-07-18T00:59:54Z")

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Thank you! This is all super helpful. Good to learn that one can pass a vector as constraints.

Unfortunately, I’m still a bit stuck. I would like to find the factors that contribute to the onset time. In particular, in my full model in which t\_O is integrated out, the variance of the onset distribution is constant (1 parameter, homoscedastic), but the mean of the onset distribution is defined as a function O\_{mean}= \alpha + \beta \cdot x where the parameters are the intercept \alpha and \beta coefficients and x is the “design matrix” of observations associated with the predictor variables. So, I am unclear how to constrain the t\_O values when they are defined in terms of a function of predictor variables. This is a bit like a simplex in which the set of values is constrained so that the weighted sum of them is less than t. But in this case, I fear the manifold may be a bit more complex than a simplex, but I really haven’t figured this out. I alluded to this issue in my [first post](https://discourse.mc-stan.org/t/defining-an-implicit-prior-on-an-implicit-manifold-in-rstan/31932), although my thinking has progressed a lot since that time, but the core issue persists. Is there a way to put “joint” constraints on parameters so that a function of the parameters is constrained to be less than a particular value? Or, is there a better way to implement this?

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