Hi,
I’m new to Gaussian Processes and I want to extend the model from chapter 17.4 to the multivariate case.

Here is what I came up with:

model_string_gp <-"
data {
int<lower=1> D;
int<lower=1> N1;
int<lower=1> N2;
vector[D] x1[N1];
vector[N1] y1;
vector[D] x2[N2];
}
transformed data {
int<lower=1> N;
vector[D] x[N1+N2];
vector[N1+N2] mu;
matrix[N1+N2, N1+N2] Sigma;
//cov_matrix[N1+N2] Sigma;
N = N1 + N2;
for (n in 1:N1) x[n] = x1[n];
for (n in 1:N2) x[N1 + n] = x2[n];
for (i in 1:N) mu[i] = 0;
for (i in 1:N)
for (j in 1:N)
Sigma[i, j] = exp(-dot_self(x[i] - x[j]))
+ i == j ? 0.1 : 0.0;
}
parameters {
vector[N2] y2;
}
model {
vector[N] y;
for (n in 1:N1) y[n] = y1[n];
for (n in 1:N2) y[N1 + n] = y2[n];
y ~ multi_normal(mu, Sigma);
}
"

I changed “cov_matrix[N1+N2] Sigma” to a simple matrix because I was getting errors being not symmetrical.
When I fit this model to some data, I run into these errors:

Rejecting initial value:
Error evaluating the log probability at the initial value.
Rejecting initial value:
Error evaluating the log probability at the initial value.
Initialization between (-2, 2) failed after 100 attempts.
Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
[1] "Error in sampler$call_sampler(args_list[[i]]) : Initialization failed."

I changed the “init_r” but it changed nothing. The univariate model from the docs runs fine.

The + gets evaluated before the == right (this code is straight from page 250 of the 2.15 manual)? I guess this is all gonna be replaced by @rtrangucci 's stuff in the next manual?

thanks, that seems to fix the problem. I changed the parenthesis and it worked. I guess that needs to be fixed in the docs as I just copy/pasted this line from there.

Also, for radial basis function Gaussian processes, check out the function cov_exp_quad in the docs. It lets you build a covariance matrix with one line of code. It’s really handy cause sometimes code for GPs can get out of hand (there’s some examples using it here: https://github.com/stan-dev/stancon_talks/tree/master/2017/Contributed-Talks/08_trangucci).

In that case, if you want to add stuff to the diagonal, you’ll need to use the second loop as well. cov_exp_quad might be a bit faster too.