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Update 9_4_Bayesian_Approach.ipynb

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Pietro Monticone
2023-10-30 18:04:23 +01:00
parent 94df10a9ec
commit 4f2d3f31f0
1 changed files with 3 additions and 3 deletions
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Notebooks/Chap09/9_4_Bayesian_Approach.ipynb
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@@ -80,7 +80,7 @@
" for i in range(n_data):\n", " for i in range(n_data):\n",
" x[i] = np.random.uniform(i/n_data, (i+1)/n_data, 1)\n", " x[i] = np.random.uniform(i/n_data, (i+1)/n_data, 1)\n",
"\n", "\n",
" # y value from running through functoin and adding noise\n", " # y value from running through function and adding noise\n",
" y = np.ones(n_data)\n", " y = np.ones(n_data)\n",
" for i in range(n_data):\n", " for i in range(n_data):\n",
" y[i] = true_function(x[i])\n", " y[i] = true_function(x[i])\n",
@@ -137,7 +137,7 @@
"n_data = 15\n", "n_data = 15\n",
"x_data,y_data = generate_data(n_data, sigma_func)\n", "x_data,y_data = generate_data(n_data, sigma_func)\n",
"\n", "\n",
"# Plot the functinon, data and uncertainty\n", "# Plot the function, data and uncertainty\n",
"plot_function(x_func, y_func, x_data, y_data, sigma_func=sigma_func)" "plot_function(x_func, y_func, x_data, y_data, sigma_func=sigma_func)"
], ],
"metadata": { "metadata": {
@@ -357,7 +357,7 @@
"\n", "\n",
"To compute this, we reformulated the integrand using the relations from appendices\n", "To compute this, we reformulated the integrand using the relations from appendices\n",
"C.3.3 and C.3.4 as the product of a normal distribution in $\\boldsymbol\\phi$ and a constant with respect\n", "C.3.3 and C.3.4 as the product of a normal distribution in $\\boldsymbol\\phi$ and a constant with respect\n",
"to $\\boldsymbol\\phi$. The integral of the normal distribution must be one, and so the finnal result is just the constant. This constant is itself a normal distribution in $y^*$. <br>\n", "to $\\boldsymbol\\phi$. The integral of the normal distribution must be one, and so the final result is just the constant. This constant is itself a normal distribution in $y^*$. <br>\n",
"\n", "\n",
"If you feel so inclined you can work through the math of this yourself." "If you feel so inclined you can work through the math of this yourself."
], ],