Selecting rows/columns of a matrix

[Luis Usier]

Hi Stan,

I am trying to set up a gaussian process regression model to predict the performance of football teams. In the model, each team has an intrinsic ability level theta that varies as a gaussian process over a number of seasons. The full code is here: 

"

data {

  int<lower=1> matches;

  int<lower=2> teams;

  int<lower=3> levels;

  int<lower=1> seasons;

  int<lower=1,upper=teams> home[matches,seasons];

  int<lower=1,upper=teams> away[matches,seasons];

  int<lower=1,upper=levels> results[matches,seasons];

  int<lower=0,upper=1> div[teams,seasons];

}

parameters {

  ordered[levels-1] c;

  matrix[teams,seasons] theta;

  real mu_rel;

  real<lower=0> rho_sq;

}

model {

  real gamma;

  vector[levels] d;

  vector[seasons] mu;

  matrix[seasons,seasons] Sigma;

  for (team in 1:teams){

    for (i in 1:seasons){

      for (j in 1:seasons){

        Sigma[i,j] <- exp(-rho_sq * pow(theta[team,i] - theta[team,j],2));

      }

    }

    for (k in 1:seasons){

      if (div[team,k] == 1){

        mu[k] <- 0;

      }

      if (div[team,k] == 0){

        mu[k] <- mu_rel;

      }

    theta[team] ~ multi_normal(mu,Sigma);

    }

  }

  for (season in 1:seasons){

    for (match in 1:matches){

      gamma <- theta[home[match,season],season] - theta[away[match,season],season];

  

      d[1] <- 1 - inv_logit(gamma - c[1]);

      for (level in 2:(levels-1))

        d[level] <- inv_logit(gamma - c[level-1]) - inv_logit(gamma - c[level]);

      d[levels] <- inv_logit(gamma - c[levels-1]);

      

      results[match,season] ~ categorical(d);

    }

  }

}

"

The model compiles just fine, but it doesn't run appropriately. When I try to sample from it, I get the following error message:

Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

stan::prob::multi_normal_log(N4stan5agrad3varE): Location parameter[2]  is nan:0, but must be finite!

I kind of know where the issue is. I have a matrix with dimensions teams x seasons, and I want to sample from a multi normal for one team at a time, i.e., one row at a time. In R, for instance, one could select the first row of an a x b matrix with mat[1,]. I do not know how to do the equivalent in stan, or even whether it is possible. In any case, the problematic line of code is: 

theta[team] ~ multi_normal(mu,Sigma);

theta is a matrix; I want to select the row team. mu should be a n-dimensional vector, and Sigma an n by n covariance matrix

Anyone has any ideas how to fix this?

[Ben Goodrich]

row(theta, team)

Ben

[Luis Usier]

Thanks a lot Ben! It seems like that is not enough to solve the issue though. I still get this error message: 

Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

stan::prob::multi_normal_log(N4stan5agrad3varE): Location parameter[2]  is nan:0, but must be finite!

I assume that this error message means the mean vector is not actually a vector, so when stan tries to access the second element of the array it breaks down; I'm not sure though. The line where I am stuck now reads: 

row(theta,team) ~ multi_normal(mu,Sigma);

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[Ben Goodrich]

It's an informational message rather than an error message, which indicates a proposal overflowed. It subsequently said not to worry if it just happens a few times. So,
is there anything else that suggests the sampler is not working in your case?

Ben

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[Marcus Brubaker]

The multi_normal sampling statement is in the wrong set of braces, it's inside the loop over k, so the values of mu aren't getting set properly.

Cheers,

Marcus

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