empirical_bayes {baldur} R Documentation

## Baldur's empirical Bayes Prior For The Mean In Conditions

### Description

Here we assume that the sample mean of each condition is an estimator for the center of the mean prior. In addition, it assumes that the confidence in the prior is proportional to the variance of the peptide.

\boldsymbol{\mu}_0\sim\mathcal{N}(\boldsymbol{\bar{y}},\sigma\boldsymbol{n}_R)

\boldsymbol{n}_R=[\frac{1}{\sqrt{n_1}},\frac{1}{\sqrt{n_2}},\dots,\frac{1}{\sqrt{n_C}}]

### Value

A stanmodel that can be used in infer_data_and_decision_model.

### Code

The Stan code for this model is given by:

empirical_bayes
S4 class stanmodel 'empirical_bayes' coded as follows:
data {
int<lower=0> N;     // number of data items
int<lower=0> K;     // number of conditions
int C;              // number of comparisons to perform
matrix[N, K] x;     // design matrix
vector[N] y;        // data
matrix[K, C] c;     // contrast matrix
real alpha;         // alpha prior for gamma
real beta;          // beta prior for gamma
vector[N] u;        // uncertainty
vector[K] mu_not;   // prior mu
}
transformed data{
vector[K] n_k;      // per condition reciprocal measurements
row_vector[C] n_c;  // per comparison measurements
matrix[K, C] abs_c; // abs of C for n_c calculation
for (i in 1:K) {
for (j in 1:C) {
abs_c[i, j] = abs(c[i, j]);
}
}
for (i in 1:K) {
n_k[i] = 1/sum(x[,i]);
}
n_c = n_k' * abs_c;
n_c = sqrt(n_c);
n_k = sqrt(2*n_k);
}
parameters {
vector[K] mu;           // mean vector
real<lower=0> sigma;    // error scale
array[C] real y_diff;   // difference in coefficients
vector[K] eta;          // Error in mean
vector[K] prior_mu_not; // Estimation error
}
transformed parameters{
row_vector[C] mu_diff = mu' * c;      // differences in means
vector[K] sigma_mu_not = sigma * n_k; // variance of ybars
vector[C] sigma_lfc = sigma * n_c';   // variance of y_diff
}
model {
sigma        ~ gamma(alpha, beta);                        // variance
eta          ~ normal(0, 1);                              // NCP auxilary variable
prior_mu_not ~ normal(mu_not, sigma_mu_not);              // Prior mean
mu           ~ normal(prior_mu_not + sigma * eta, sigma); // mean
y            ~ normal(x * mu, sigma * u);                 // data model
y_diff       ~ normal(mu_diff, sigma_lfc);                // difference statistic
}


[Package baldur version 0.0.3 Index]