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# mrecos/GP_estimate_eta_rho_SE.stan

Created May 27, 2016 17:52
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stan code for estimating eta and rho hyperparameters of the squared exponential kernel within a Gaussian Process.
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 // Predict from Gaussian Process // estimate sigma_sq and rho_sq // All data parameters must be passed as a list to the Stan call // Based on original file from https://code.google.com/p/stan/source/browse/src/models/misc/gaussian-process/ data { int N1; vector[N1] x1; vector[N1] y1; int N2; vector[N2] x2; real sigma_sq; } transformed data { int N; vector[N1+N2] x; vector[N1+N2] mu; 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; } parameters { vector[N2] y2; real rho_sq; real eta_sq; } transformed parameters { } model { vector[N] y; matrix[N, N] Sigma; // off-diagonal elements for (i in 1:(N-1)){ for (j in (i+1):N){ //// Squared Exponential (RBF) Kerenl Sigma[i,j] <- eta_sq * exp(-rho_sq * pow(x[i] - x[j],2)); Sigma[j,i] <- Sigma[i,j]; } } // diagonal elements for (k in 1:N){ Sigma[k,k] <- 1 + sigma_sq; // + jitter } rho_sq ~ cauchy(0,5); eta_sq ~ cauchy(0,5); for (n in 1:N1) y[n] <- y1[n]; for (n in 1:N2) y[N1 + n] <- y2[n]; y ~ multi_normal(mu,Sigma); }
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