Document variance correction for sum to zero matrix

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Assessment

Difficulty
2/5
Estimated time
1-3 hours
Newbie friendliness
68/100
Issue type
Documentation
Clarity
Mostly clear
Activity status
Active
Tech stack
tex
Domain
documentation

Research direction

Start by locating the Stan manual section covering sum-to-zero transforms and the existing documentation for the supplied correction. Add the variance formula and its matrix and N-dimensional tensor context, then verify that the manual renders and the documented correction matches the issue's example.

Written by the indexing model from the issue text.

Description

Mostly a reminder for @spinkney who said he would add this on slack

Message

I need to add this to the manual. An N-dimensional tensor with variance tau^2 where each dimension sums to 0 through an isotropic sum-to-zero transform will have variance of tau^2 * prod( (d_k - 1) / d_k) so to correct you need tau^2 * prod(d_k / (d_k - 1)) as the correction.

I deliberately coded this to take in the dimensions to be suitable for a sum-to-zero N-d array but it works fine for matrix

functions {
    real s2z_unit_normal_correction (array[] int s2z_dims) {
        int N = num_elements(s2z_dims);
        vector[N] d = to_vector(s2z_dims);
        return sqrt(prod(d ./ (d - 1)));
    }

    real s2z_unit_normal_lpdf (vector z, array[] int s2z_dims) {
        int N = num_elements(s2z_dims);
        vector[N] d = to_vector(s2z_dims);
        return -dot_self(z) + N * 2 * prod(d ./ (d - 1));
    }
}
data {
    int<lower=1> N;
    int<lower=1> M;
    int<lower=0, upper=1> flag;
}
parameters {
    sum_to_zero_matrix[N, M] X;
}
model {
  if (flag == 0) {
    to_vector(X) ~ normal(0, s2z_unit_normal_correction(dims(X)));
  } else {
    to_vector(X) ~ s2z_unit_normal(dims(X));
  }
}

Dominant language
TeX
Stars
43
Forks
133
Avg merge
11h 32m
Merged PRs (30d)
4

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