dr_domi/udlbook
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Fix more Chap09 tiny typos

Browse Source
This commit is contained in:
Youcef Rahal
2024-05-11 15:20:11 -04:00
parent 1343b68c60
commit 2ac42e70d3
1 changed files with 4 additions and 4 deletions
Download Patch File Download Diff File Expand all files Collapse all files

6
Notebooks/Chap09/9_4_Bayesian_Approach.ipynb
View File

@@ -36,7 +36,7 @@
"# import libraries\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"# Define seed so get same results each time\n",
"# Define seed to get same results each time\n",
"np.random.seed(1)"
]
},
@@ -85,7 +85,7 @@
},
"outputs": [],
"source": [
"# Draw the fitted function, together win uncertainty used to generate points\n",
"# Draw the fitted function, together with uncertainty used to generate points\n",
"def plot_function(x_func, y_func, x_data=None,y_data=None, x_model = None, y_model =None, sigma_func = None, sigma_model=None):\n",
"\n",
" fig,ax = plt.subplots()\n",
@@ -220,7 +220,7 @@
" &\\propto&\\text{Norm}_{\\boldsymbol\\phi}\\biggl[\\frac{1}{\\sigma^2}\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\\mathbf{H}\\mathbf{y},\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\\biggr].\n",
"\\end{align}\n",
"\n",
"In fact, since this already a normal distribution, the constant of proportionality must be one and we can write\n",
"In fact, since this is already a normal distribution, the constant of proportionality must be one and we can write\n",
"\n",
"\\begin{align}\n",
" Pr(\\boldsymbol\\phi|\\{\\mathbf{x}_{i},\\mathbf{y}_{i}\\}) &=& \\text{Norm}_{\\boldsymbol\\phi}\\biggl[\\frac{1}{\\sigma^2}\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\\mathbf{H}\\mathbf{y},\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\\biggr].\n",