posterior mean vis

docs/texs/matern_mcmc.tex

@@ -61,7 +61,7 @@ Let's consider a model:
 \end{gather}
 where \(\mathbf{y}\) is an observed field, \(\mathbf{z}\) is a hidden field, and 
 \(\mathcal{K}\) is a Mat\'{e}rn covariance function with parameters 
-\(\theta = (\sigma, l, \sigma)\):
+\(\theta = (\nu, l, \sigma)\):
 \begin{equation}
     \mathcal{K}(\rho) = 
     \frac{\sigma^2 2^{1 - \nu}}{\Gamma(\nu)}
@@ -70,7 +70,7 @@ where \(\mathbf{y}\) is an observed field, \(\mathbf{z}\) is a hidden field, and
     \right)^{\nu}
     K_{\nu} \left(
         \frac{\sqrt{2\nu} \rho}{l}
-    \right)^{\nu},
+    \right),
 \end{equation}
 where \(\Gamma\) is the gamma function and \(K_{\nu}\) is the modified Bessel function of the second kind.
 
@@ -107,7 +107,7 @@ where \(\Gamma\) is the gamma function and \(K_{\nu}\) is the modified Bessel fu
     \subfloat[]{\includegraphics[width=0.30\textwidth]{k_smooth_2_1}}
     \hfil
     \subfloat[]{\includegraphics[width=0.30\textwidth]{k_smooth_2_2}}
-    \caption{Sampled Mat\'{e}rn dields for rows: \( \nu = 0.5 \), 
+    \caption{Sampled Mat\'{e}rn fields for rows: \( \nu = 0.5 \), 
     \( \nu = 1 \), \( \nu = 2.5 \). For all samples \( \sigma = 1 \)
     and \( l = 2 \).}
     \label{fig:samples}

dummy_estimate_matern.py

@@ -14,6 +14,8 @@ def main():
     with open('./data/field.pickle', 'rb') as f:
         xs, ys, field, nu, sigma, l = pickle.load(f)
 
+    w, h = np.size(xs), np.size(ys)
+
     print("Pre-evaluating distance matrix")
     dist_mtx = rf.dist_matrix(xs, ys)
     flat_gt_field = np.ravel(field)
@@ -22,7 +24,7 @@ def main():
     noise = np.random.normal(scale=noise_sigma, size=flat_gt_field.shape)
 
     initial_field = flat_gt_field + noise
-    initial_theta = np.array([nu, sigma, l]) + 1e-2
+    initial_theta = np.array([nu, sigma, l]) + 0.7
 
     proposal_cov = 1e-4 * np.eye(3)
     lower = np.array([0.5, 0.5, 0.5])
@@ -37,6 +39,21 @@ def main():
     with open('./data/matern_chain.pickle', 'wb') as f:
         pickle.dump(chain_res, f)
 
+    chain, p_accs, nlls = chain_res
+    theta_chain, field_chain = zip(*chain)
+    figs_outpath = './figs/dummy_matern/'
+    os.makedirs(figs_outpath, exist_ok=True)
+    rf.show_theta_chain(theta_chain, p_accs, nlls, figs_outpath)
+    field_mean, _ = rf.estimate_field_norm_posterior(field_chain, w, h, figs_outpath)
+
+    field_err = field - field_mean
+    plt.figure()
+    plt.imshow(field_err)
+    plt.colorbar()
+    plt.title("GT - mean estimate")
+    plt.savefig(os.path.join(figs_outpath, "field_err.png"))
+    plt.close()
+
 
 if __name__ == '__main__':
     random.seed(42)

dummy_margl_sampling.py

@@ -38,7 +38,7 @@ def main():
         lower=lower, upper=upper
     )
 
-    with open('./data/matern_chain.pickle', 'wb') as f:
+    with open('./data/margl_chain.pickle', 'wb') as f:
         pickle.dump(chain_res, f)
 
     chain, p_accs, nlls = chain_res