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12-sparse_horseshoe_p_regression.stan
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// run with 4 chains and 2k iters.
// all data should be scaled to mean 0 and std 1:
// sparse_regression data
data {
int<lower=1> N; // number of observations
int<lower=1> K; // number of independent variables
matrix[N, K] X; // data matrix
vector[N] y; // dependent variable vector
}
parameters {
real alpha; // intercept
vector<lower=0>[K] lambda; // local shrinkage factor
real<lower=0> eta; // additional local shrinkage factor
real<lower=0> sigma; // model error
real<lower=0> tau; // global shinkrage factor
vector[K] beta; // coefficients for independent variables
}
model {
// priors
alpha ~ student_t(3, 0, 2.5);
lambda ~ cauchy(0, 1);
sigma ~ exponential(1);
tau ~ cauchy(0, (1 / K) + machine_precision()); // numerical stability
eta ~ cauchy(0, 1);
beta ~ normal(0, lambda * tau * eta);
// likelihood
y ~ normal(alpha + X * beta, sigma);
}
// results:
//Warmup took (2.2, 2.2, 2.1, 2.2) seconds, 8.7 seconds total
//Sampling took (2.2, 2.2, 2.4, 3.0) seconds, 9.8 seconds total
// Mean MCSE StdDev 5% 50% 95% N_Eff N_Eff/s R_hat
//lp__ -1.2e+02 1.6e-01 5.6e+00 -1.3e+02 -1.2e+02 -1.1e+02 1194 122 1.0
//accept_stat__ 0.92 3.6e-03 1.3e-01 6.7e-01 0.97 1.00 1366 139 1.0e+00
//stepsize__ 0.010 7.2e-04 1.0e-03 8.3e-03 0.011 0.011 2.0 0.20 2.5e+13
//treedepth__ 8.3 2.3e-01 6.2e-01 8.0e+00 8.0 9.0 7.1 0.73 1.2e+00
//n_leapfrog__ 401 4.1e+01 1.4e+02 2.6e+02 511 511 12 1.3 1.1e+00
//divergent__ 0.036 3.5e-03 1.9e-01 0.0e+00 0.00 0.00 2804 286 1.0e+00
//energy__ 145 2.2e-01 7.3e+00 1.3e+02 145 158 1119 114 1.0e+00
//alpha 1.1e-01 2.3e-03 1.1e-01 -6.9e-02 1.1e-01 2.9e-01 2278 232 1.0
//lambda[1] 1.1e+01 4.0e-01 1.7e+01 2.3e+00 7.1e+00 3.4e+01 1774 181 1.00
//lambda[2] 8.5e-01 3.1e-02 1.7e+00 3.9e-02 4.8e-01 2.6e+00 2985 304 1.00
//lambda[3] 6.3e+00 2.1e-01 8.8e+00 1.3e+00 4.0e+00 1.7e+01 1688 172 1.0
//lambda[4] 8.9e-01 3.6e-02 1.9e+00 5.2e-02 5.0e-01 2.6e+00 2601 265 1.0
//lambda[5] 7.5e+00 3.4e-01 1.3e+01 1.5e+00 4.7e+00 2.0e+01 1345 137 1.0
//lambda[6] 5.0e+00 1.8e-01 7.2e+00 1.1e+00 3.2e+00 1.4e+01 1680 171 1.0
//lambda[7] 9.7e-01 3.6e-02 1.8e+00 5.6e-02 5.8e-01 2.9e+00 2408 246 1.0
//lambda[8] 3.4e+00 1.7e-01 6.1e+00 6.7e-01 2.1e+00 9.5e+00 1324 135 1.0
//lambda[9] 9.5e-01 8.0e-02 4.8e+00 4.3e-02 4.6e-01 2.8e+00 3623 370 1.0
//lambda[10] 1.1e+00 5.3e-02 2.3e+00 4.3e-02 5.8e-01 3.5e+00 1988 203 1.0
//lambda[11] 1.9e+00 5.6e-02 2.6e+00 2.2e-01 1.1e+00 5.5e+00 2167 221 1.0
//lambda[12] 9.5e-01 4.5e-02 1.9e+00 4.8e-02 5.1e-01 3.0e+00 1760 180 1.0
//lambda[13] 8.9e-01 2.6e-02 1.4e+00 5.5e-02 5.3e-01 2.7e+00 2697 275 1.0
//lambda[14] 9.5e+00 4.1e-01 1.5e+01 2.0e+00 6.0e+00 2.6e+01 1266 129 1.0
//lambda[15] 1.0e+00 4.2e-02 1.9e+00 4.8e-02 5.9e-01 3.1e+00 1918 196 1.0
//lambda[16] 8.6e-01 3.3e-02 1.5e+00 3.5e-02 4.9e-01 2.8e+00 2012 205 1.0
//
//lambda[17] 8.2e-01 3.0e-02 1.4e+00 3.5e-02 4.6e-01 2.6e+00 2278 232 1.0
//lambda[18] 8.6e-01 2.7e-02 1.2e+00 4.7e-02 5.0e-01 2.8e+00 2082 212 1.0
//lambda[19] 8.3e-01 3.1e-02 1.5e+00 4.8e-02 4.6e-01 2.5e+00 2250 230 1.0
//lambda[20] 9.4e+00 6.0e-01 2.5e+01 1.9e+00 5.9e+00 2.5e+01 1694 173 1.0
//eta 3.6e+13 3.9e+12 2.0e+14 7.0e+00 6.6e+07 1.4e+14 2599 265 1.0
//sigma 9.6e-01 1.5e-03 7.5e-02 8.5e-01 9.5e-01 1.1e+00 2496 255 1.0
//tau 8.3e-03 1.3e-03 7.8e-02 1.2e-15 2.7e-09 2.7e-02 3855 393 1.00
//beta[1] 1.4e+00 2.2e-03 1.0e-01 1.2e+00 1.4e+00 1.6e+00 2189 223 1.0
//beta[2] 2.0e-02 1.5e-03 6.8e-02 -8.1e-02 8.3e-03 1.4e-01 2164 221 1.0
//beta[3] 7.5e-01 2.1e-03 1.1e-01 5.7e-01 7.5e-01 9.3e-01 2662 272 1.00
//beta[4] 2.6e-02 1.5e-03 7.2e-02 -7.7e-02 1.4e-02 1.6e-01 2218 226 1.0
//beta[5] -8.9e-01 1.9e-03 1.1e-01 -1.1e+00 -8.9e-01 -7.1e-01 3191 326 1.0
//beta[6] 5.8e-01 2.0e-03 1.0e-01 4.1e-01 5.8e-01 7.4e-01 2633 269 1.00
//beta[7] 5.0e-02 1.9e-03 8.1e-02 -5.7e-02 3.3e-02 2.1e-01 1767 180 1.0
//beta[8] 3.7e-01 1.9e-03 1.0e-01 2.0e-01 3.6e-01 5.3e-01 2848 291 1.0
//beta[9] -7.3e-03 1.6e-03 7.2e-02 -1.4e-01 -2.2e-03 1.1e-01 2008 205 1.0
//beta[10] 5.1e-02 2.0e-03 8.2e-02 -5.6e-02 3.2e-02 2.1e-01 1755 179 1.0
//beta[11] 1.8e-01 2.7e-03 1.1e-01 -2.0e-03 1.8e-01 3.6e-01 1762 180 1.0
//beta[12] -2.7e-02 1.7e-03 7.6e-02 -1.7e-01 -1.4e-02 8.6e-02 1874 191 1.0
//beta[13] -2.9e-02 1.8e-03 7.7e-02 -1.8e-01 -1.6e-02 8.3e-02 1877 191 1.0
//beta[14] -1.1e+00 1.8e-03 9.7e-02 -1.3e+00 -1.1e+00 -9.7e-01 2840 290 1.0
//beta[15] -5.0e-02 2.3e-03 8.9e-02 -2.2e-01 -3.0e-02 7.3e-02 1537 157 1.0
//beta[16] -1.7e-02 1.5e-03 7.2e-02 -1.5e-01 -7.4e-03 9.6e-02 2251 230 1.0
//beta[17] -1.0e-02 1.4e-03 6.6e-02 -1.2e-01 -3.4e-03 9.4e-02 2331 238 1.0
//beta[18] 2.1e-02 1.6e-03 7.0e-02 -8.4e-02 9.3e-03 1.5e-01 2032 207 1.0
//beta[19] -9.5e-04 1.3e-03 6.1e-02 -1.0e-01 -5.3e-05 9.8e-02 2095 214 1.00
//beta[20] -1.1e+00 2.3e-03 1.2e-01 -1.3e+00 -1.1e+00 -9.2e-01 2663 272 1.0