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mhjensen
2018-08-24 06:35:38 +02:00
parent 3a6bdf1450
commit dc7ce90ee7
20 changed files with 159 additions and 2504 deletions
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doc/pub/Regression/html/._Regression-bs017.html
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@@ -210,8 +210,9 @@ MathJax.Hub.Config({
<p>
For a linear fit we don't need to invert a matrix!!
Defining
$$
\gamma = \sum_{i=0}^{n-1}\frac{n-1}{\sigma_i^2},
\gamma = \sum_{i=0}^{n-1}\frac{1}{\sigma_i^2},
$$
@@ -231,7 +232,7 @@ $$
\gamma_{xy} = \sum_{i=0}^{n-1}\frac{y_ix_{i}}{\sigma_i^2},
$$
and show that
we obtain
$$
\beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2},
$$
@@ -241,7 +242,7 @@ $$
$$
<p>
The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \). A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
This approach (different linear and non-linear regression) suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \). A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
</div>
</div>
doc/pub/Regression/html/Regression-reveal.html
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@@ -646,11 +646,11 @@ $$
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<p>
For a linear fit we don't need to invert a matrix!!
For a linear fit we don't need to invert a matrix!!
Defining
<p>&nbsp;<br>
$$
\gamma = \sum_{i=0}^{n-1}\frac{n-1}{\sigma_i^2},
\gamma = \sum_{i=0}^{n-1}\frac{1}{\sigma_i^2},
$$
<p>&nbsp;<br>
@@ -678,7 +678,7 @@ $$
$$
<p>&nbsp;<br>
and show that
we obtain
<p>&nbsp;<br>
$$
\beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2},
@@ -692,7 +692,7 @@ $$
<p>&nbsp;<br>
<p>
The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \). A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
This approach (different linear and non-linear regression) suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \). A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
</div>
</section>
doc/pub/Regression/html/Regression-solarized.html
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@@ -616,8 +616,9 @@ $$
<p>
For a linear fit we don't need to invert a matrix!!
Defining
$$
\gamma = \sum_{i=0}^{n-1}\frac{n-1}{\sigma_i^2},
\gamma = \sum_{i=0}^{n-1}\frac{1}{\sigma_i^2},
$$
@@ -637,7 +638,7 @@ $$
\gamma_{xy} = \sum_{i=0}^{n-1}\frac{y_ix_{i}}{\sigma_i^2},
$$
and show that
we obtain
$$
\beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2},
$$
@@ -647,7 +648,7 @@ $$
$$
<p>
The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \). A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
This approach (different linear and non-linear regression) suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \). A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
</div>
doc/pub/Regression/html/Regression.html
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@@ -621,8 +621,9 @@ $$
<p>
For a linear fit we don't need to invert a matrix!!
Defining
$$
\gamma = \sum_{i=0}^{n-1}\frac{n-1}{\sigma_i^2},
\gamma = \sum_{i=0}^{n-1}\frac{1}{\sigma_i^2},
$$
@@ -642,7 +643,7 @@ $$
\gamma_{xy} = \sum_{i=0}^{n-1}\frac{y_ix_{i}}{\sigma_i^2},
$$
and show that
we obtain
$$
\beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2},
$$
@@ -652,7 +653,7 @@ $$
$$
<p>
The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \). A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
This approach (different linear and non-linear regression) suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \). A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
</div>
doc/pub/Regression/ipynb/Regression.ipynb
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@@ -745,7 +745,8 @@
"source": [
"## The $\\chi^2$ function\n",
"\n",
"For a linear fit we don't need to invert a matrix!!"
"For a linear fit we don't need to invert a matrix!! \n",
"Defining"
]
},
{
@@ -753,7 +754,7 @@
"metadata": {},
"source": [
"$$\n",
"\\gamma = \\sum_{i=0}^{n-1}\\frac{n-1}{\\sigma_i^2},\n",
"\\gamma = \\sum_{i=0}^{n-1}\\frac{1}{\\sigma_i^2},\n",
"$$"
]
},
@@ -842,7 +843,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"and show that"
"we obtain"
]
},
{
@@ -882,7 +883,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients $\\beta_i$. A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.\n",
"This approach (different linear and non-linear regression) suffers often from both being underdetermined and overdetermined in the unknown coefficients $\\beta_i$. A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.\n",
"\n",
"\n",
"\n",
doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz
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doc/pub/Regression/pdf/Regression-beamer-handouts2x3.pdf
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doc/pub/Statistics/html/Statistics-bs.html
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doc/pub/Statistics/html/Statistics-reveal.html
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@@ -163,7 +163,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>&nbsp;<br>
<center><h4>May 22, 2018</h4></center> <!-- date -->
<center><h4>Aug 24, 2018</h4></center> <!-- date -->
<br>
<p>
@@ -176,6 +176,7 @@ MathJax.Hub.Config({
<section>
<h2 id="___sec0">Things to add </h2>
Add general statistic elements (probability theory mainly), assumed knowledge
Repeat basic definitions.
</section>
@@ -609,16 +610,16 @@ while \( P(x) \) is the cumulative probability.
<p>
<table border="1">
<thead>
<tr><th align="center"> </th> <th align="center"> Discrete PDF </th> <th align="center"> Continuous PDF </th> </tr>
<tr><th align="center"> </th> <th align="center"> Discrete PDF </th> <th align="center"> Continuous PDF </th> </tr>
</thead>
<tbody>
<tr><td align="left"> Domain </td> <td align="center"> \( \left\{x_1, x_2, x_3, \dots, x_N\right\} \) </td> <td align="center"> \( [a,b] \) </td> </tr>
<tr><td align="left"> Probability </td> <td align="center"> \( p(x_i) \) </td> <td align="center"> \( p(x)dx \) </td> </tr>
<tr><td align="left"> Cumulative </td> <td align="center"> \( P_i=\sum_{l=1}^ip(x_l) \) </td> <td align="center"> \( P(x)=\int_a^xp(t)dt \) </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0\le p(x_i)\le 1$ </td> <td align="center"> $ p(x) \ge 0$ </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0\le P_i\le 1$ </td> <td align="center"> $ 0\le P(x)\le 1$ </td> </tr>
<tr><td align="left"> Monotonic </td> <td align="center"> \( P_i\ge P_j \) if \( x_i\ge x_j \) </td> <td align="center"> \( P(x_i)\ge P(x_j) \) if \( x_i\ge x_j \) </td> </tr>
<tr><td align="left"> Normalization </td> <td align="center"> \( P_N=1 \) </td> <td align="center"> \( P(b)=1 \) </td> </tr>
<tr><td align="left"> Domain </td> <td align="center"> \( \left\{x_1, x_2, x_3, \dots, x_N\right\} \) </td> <td align="center"> \( [a,b] \) </td> </tr>
<tr><td align="left"> Probability </td> <td align="center"> \( p(x_i) \) </td> <td align="center"> \( p(x)dx \) </td> </tr>
<tr><td align="left"> Cumulative </td> <td align="center"> \( P_i=\sum_{l=1}^ip(x_l) \) </td> <td align="center"> \( P(x)=\int_a^xp(t)dt \) </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0 \le p(x_i) \le 1$ </td> <td align="center"> $ p(x) \ge 0$ </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0 \le P_i \le 1$ </td> <td align="center"> $ 0 \le P(x) \le 1$ </td> </tr>
<tr><td align="left"> Monotonic </td> <td align="center"> \( P_i \ge P_j \) if \( x_i \ge x_j \) </td> <td align="center"> \( P(x_i) \ge P(x_j) \) if \( x_i \ge x_j \) </td> </tr>
<tr><td align="left"> Normalization </td> <td align="center"> \( P_N=1 \) </td> <td align="center"> \( P(b)=1 \) </td> </tr>
</tbody>
</table>
doc/pub/Statistics/html/Statistics-solarized.html
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@@ -322,13 +322,14 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>May 22, 2018</h4></center> <!-- date -->
<center><h4>Aug 24, 2018</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec0">Things to add </h2>
Add general statistic elements (probability theory mainly), assumed knowledge
Repeat basic definitions.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -741,16 +742,16 @@ while \( P(x) \) is the cumulative probability.
<p>
<table border="1">
<thead>
<tr><th align="center"> </th> <th align="center"> Discrete PDF </th> <th align="center"> Continuous PDF </th> </tr>
<tr><th align="center"> </th> <th align="center"> Discrete PDF </th> <th align="center"> Continuous PDF </th> </tr>
</thead>
<tbody>
<tr><td align="left"> Domain </td> <td align="center"> \( \left\{x_1, x_2, x_3, \dots, x_N\right\} \) </td> <td align="center"> \( [a,b] \) </td> </tr>
<tr><td align="left"> Probability </td> <td align="center"> \( p(x_i) \) </td> <td align="center"> \( p(x)dx \) </td> </tr>
<tr><td align="left"> Cumulative </td> <td align="center"> \( P_i=\sum_{l=1}^ip(x_l) \) </td> <td align="center"> \( P(x)=\int_a^xp(t)dt \) </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0\le p(x_i)\le 1$ </td> <td align="center"> $ p(x) \ge 0$ </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0\le P_i\le 1$ </td> <td align="center"> $ 0\le P(x)\le 1$ </td> </tr>
<tr><td align="left"> Monotonic </td> <td align="center"> \( P_i\ge P_j \) if \( x_i\ge x_j \) </td> <td align="center"> \( P(x_i)\ge P(x_j) \) if \( x_i\ge x_j \) </td> </tr>
<tr><td align="left"> Normalization </td> <td align="center"> \( P_N=1 \) </td> <td align="center"> \( P(b)=1 \) </td> </tr>
<tr><td align="left"> Domain </td> <td align="center"> \( \left\{x_1, x_2, x_3, \dots, x_N\right\} \) </td> <td align="center"> \( [a,b] \) </td> </tr>
<tr><td align="left"> Probability </td> <td align="center"> \( p(x_i) \) </td> <td align="center"> \( p(x)dx \) </td> </tr>
<tr><td align="left"> Cumulative </td> <td align="center"> \( P_i=\sum_{l=1}^ip(x_l) \) </td> <td align="center"> \( P(x)=\int_a^xp(t)dt \) </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0 \le p(x_i) \le 1$ </td> <td align="center"> $ p(x) \ge 0$ </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0 \le P_i \le 1$ </td> <td align="center"> $ 0 \le P(x) \le 1$ </td> </tr>
<tr><td align="left"> Monotonic </td> <td align="center"> \( P_i \ge P_j \) if \( x_i \ge x_j \) </td> <td align="center"> \( P(x_i) \ge P(x_j) \) if \( x_i \ge x_j \) </td> </tr>
<tr><td align="left"> Normalization </td> <td align="center"> \( P_N=1 \) </td> <td align="center"> \( P(b)=1 \) </td> </tr>
</tbody>
</table>
doc/pub/Statistics/html/Statistics.html
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@@ -327,13 +327,14 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>May 22, 2018</h4></center> <!-- date -->
<center><h4>Aug 24, 2018</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec0">Things to add </h2>
Add general statistic elements (probability theory mainly), assumed knowledge
Repeat basic definitions.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -746,16 +747,16 @@ while \( P(x) \) is the cumulative probability.
<p>
<table border="1">
<thead>
<tr><th align="center"> </th> <th align="center"> Discrete PDF </th> <th align="center"> Continuous PDF </th> </tr>
<tr><th align="center"> </th> <th align="center"> Discrete PDF </th> <th align="center"> Continuous PDF </th> </tr>
</thead>
<tbody>
<tr><td align="left"> Domain </td> <td align="center"> \( \left\{x_1, x_2, x_3, \dots, x_N\right\} \) </td> <td align="center"> \( [a,b] \) </td> </tr>
<tr><td align="left"> Probability </td> <td align="center"> \( p(x_i) \) </td> <td align="center"> \( p(x)dx \) </td> </tr>
<tr><td align="left"> Cumulative </td> <td align="center"> \( P_i=\sum_{l=1}^ip(x_l) \) </td> <td align="center"> \( P(x)=\int_a^xp(t)dt \) </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0\le p(x_i)\le 1$ </td> <td align="center"> $ p(x) \ge 0$ </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0\le P_i\le 1$ </td> <td align="center"> $ 0\le P(x)\le 1$ </td> </tr>
<tr><td align="left"> Monotonic </td> <td align="center"> \( P_i\ge P_j \) if \( x_i\ge x_j \) </td> <td align="center"> \( P(x_i)\ge P(x_j) \) if \( x_i\ge x_j \) </td> </tr>
<tr><td align="left"> Normalization </td> <td align="center"> \( P_N=1 \) </td> <td align="center"> \( P(b)=1 \) </td> </tr>
<tr><td align="left"> Domain </td> <td align="center"> \( \left\{x_1, x_2, x_3, \dots, x_N\right\} \) </td> <td align="center"> \( [a,b] \) </td> </tr>
<tr><td align="left"> Probability </td> <td align="center"> \( p(x_i) \) </td> <td align="center"> \( p(x)dx \) </td> </tr>
<tr><td align="left"> Cumulative </td> <td align="center"> \( P_i=\sum_{l=1}^ip(x_l) \) </td> <td align="center"> \( P(x)=\int_a^xp(t)dt \) </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0 \le p(x_i) \le 1$ </td> <td align="center"> $ p(x) \ge 0$ </td> </tr>
<tr><td align="left"> Positivity </td> <td align="center"> $ 0 \le P_i \le 1$ </td> <td align="center"> $ 0 \le P(x) \le 1$ </td> </tr>
<tr><td align="left"> Monotonic </td> <td align="center"> \( P_i \ge P_j \) if \( x_i \ge x_j \) </td> <td align="center"> \( P(x_i) \ge P(x_j) \) if \( x_i \ge x_j \) </td> </tr>
<tr><td align="left"> Normalization </td> <td align="center"> \( P_N=1 \) </td> <td align="center"> \( P(b)=1 \) </td> </tr>
</tbody>
</table>
doc/pub/Statistics/ipynb
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doc/src/Regression/Regression.do.txt
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@@ -393,9 +393,10 @@ and
!bblock
For a linear fit we don't need to invert a matrix!!
Defining
!bt
\[
\gamma = \sum_{i=0}^{n-1}\frac{n-1}{\sigma_i^2},
\gamma = \sum_{i=0}^{n-1}\frac{1}{\sigma_i^2},
\]
!et
@@ -419,7 +420,7 @@ For a linear fit we don't need to invert a matrix!!
\gamma_{xy} = \sum_{i=0}^{n-1}\frac{y_ix_{i}}{\sigma_i^2},
\]
!et
and show that
we obtain
!bt
\[
\beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2},
@@ -431,7 +432,7 @@ and show that
\]
!et
The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients $\beta_i$. A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
This approach (different linear and non-linear regression) suffers often from both being underdetermined and overdetermined in the unknown coefficients $\beta_i$. A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
!eblock
doc/src/Statistics/Statistics.do.txt
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@@ -332,9 +332,9 @@ while $P(x)$ is the cumulative probability.
| Domain | $\left\{x_1, x_2, x_3, \dots, x_N\right\}$ | $[a,b]$ |
| Probability | $p(x_i)$ | $p(x)dx$ |
| Cumulative | $P_i=\sum_{l=1}^ip(x_l)$ | $P(x)=\int_a^xp(t)dt$ |
| Positivity | $ 0\le p(x_i)\le 1$ | $ p(x) \ge 0$ |
| Positivity | $ 0\le P_i\le 1$ | $ 0\le P(x)\le 1$ |
| Monotonic | $P_i\ge P_j$ if $x_i\ge x_j$ | $P(x_i)\ge P(x_j)$ if $x_i\ge x_j$ |
| Positivity | $ 0 \le p(x_i) \le 1$ | $ p(x) \ge 0$ |
| Positivity | $ 0 \le P_i \le 1$ | $ 0 \le P(x) \le 1$ |
| Monotonic | $P_i \ge P_j$ if $x_i \ge x_j$ | $P(x_i) \ge P(x_j)$ if $x_i \ge x_j$ |
| Normalization | $P_N=1$ | $P(b)=1$ |
|--------------------------------------------------------------------------------------------------------------------------------------|
doc/src/Statistics/make.sh
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@@ -44,7 +44,7 @@ system doconce split_html $html.html --method=space10
# Bootstrap style
html=${name}-bs
system doconce format html $name --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=$html $opt
#system doconce split_html $html.html --method=split --pagination --nav_button=bottom
system doconce split_html $html.html --method=split --pagination --nav_button=bottom
# IPython notebook
system doconce format ipynb $name $opt