Using a vector as a lower bound of another vector

[sepehr akhavan]

Hi,

I'm familiar with the syntax below:

vector<lower = L> myVec;

In the code above, every element of the myVec vector has a lower bound of L. Now, suppose Lvec is a vector of lower bounds where Lvec[i] is the lower bound for the ith element of myVec. I tried:

vector<lower = Lvec> myVec; 

but as I expected, it didn't work. Any easy way to do that?

Thanks very much for your help,

[Ben Goodrich]

Assuming Lvec is strictly positive, you can do

parameters {
  vector[K]<lower=1> myPrimitiveVec
}
transformed parameters
  vector[K] myVec;
  myVec <- myPrimitiveVec .* Lvec;
}

Ben

[Bob Carpenter]

No, you basically have to do the transforms yourself.

data {
int N;
vector[N] L; // lower bounds

parameters {
vector[N] my_vec_raw;


transformed parameters {
vector[N] my_vec;
my_vec <- L + exp(my_vec_raw);

model {
increment_log_prob(sum(my_vec_raw)); // Jacobian

I should at least put this in the manual until I can implement
vectors of lower bounds. I made the lower bound data here, but
it could also be a parameter itself. As long as the parameter
L isn't computed in terms of my_vec_raw, then the Jacobian above
is sufficient for the transform (L, my_vec_raw) -> (L, my_vec).

- Bob

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[Bob Carpenter]

I didn't see Ben's answer before responding. I seem to be
getting lag in the Apple mailer from other's responses. The
approach Ben offered is more straightforward; mine was just
recreating what Stan does internally for bounds.

Ben's is going to work out to

mu_vec <- L .* (exp(my_vec_raw) + 1)
...
increment_log_prob(sum(my_vec_raw));

and mine to

L + exp(my_vec_raw)
...
increment_log_prob(sum(my_vec_raw));

We still haven't studied much about how parameterizations of
various kinds affect sampling.

- Bob

[Meng Zhao]

What if Lvec is negative? For example if it is negative lower bound distribution, how can I provide lower bound for my vector? Thanks.

[Ben Goodrich]

On Wednesday, September 28, 2016 at 9:38:53 PM UTC-4, Meng Zhao wrote:

What if Lvec is negative? For example if it is negative lower bound distribution, how can I provide lower bound for my vector? Thanks.

Then you have to do the transformations yourself: exp() to get something non-negative and add Lvec to get something that is >= to Lvec.

Ben

[Bob Carpenter]

And then you need the Jacobian if you are putting
a distribution on the transformed parameter.

- Bob