diff --git a/doc/pub/week36/html/week36-bs.html b/doc/pub/week36/html/week36-bs.html index 7df89604a..3edca1169 100644 --- a/doc/pub/week36/html/week36-bs.html +++ b/doc/pub/week36/html/week36-bs.html @@ -155,6 +155,10 @@ Automatically generated HTML file from DocOnce source None, 'example-of-usage-of-bayes-theorem'), ('Doing it correctly', 2, None, 'doing-it-correctly'), + ("Bayes' Theorem and Ridge and Lasso Regression", + 2, + None, + 'bayes-theorem-and-ridge-and-lasso-regression'), ('Why resampling methods', 2, None, 'why-resampling-methods'), ('Resampling methods', 2, None, 'resampling-methods'), ('Resampling approaches can be computationally expensive', @@ -323,33 +327,34 @@ MathJax.Hub.Config({
  • Interpretations of Bayes' Theorem
  • Example of Usage of Bayes' theorem
  • Doing it correctly
    • -
  • Why resampling methods
    • -
  • Resampling methods
    • -
  • Resampling approaches can be computationally expensive
    • -
  • Why resampling methods ?
    • -
  • Statistical analysis
    • -
  • Resampling methods
    • -
  • Resampling methods: Jackknife and Bootstrap
    • -
  • Resampling methods: Jackknife
    • -
  • Jackknife code example
    • -
  • Resampling methods: Bootstrap
    • -
  • Resampling methods: Bootstrap background
    • -
  • Resampling methods: More Bootstrap background
    • -
  • Resampling methods: Bootstrap approach
    • -
  • Resampling methods: Bootstrap steps
    • -
  • Code example for the Bootstrap method
    • -
  • Various steps in cross-validation
    • -
  • How to set up the cross-validation for Ridge and/or Lasso
    • -
  • Cross-validation in brief
    • -
  • Code Example for Cross-validation and \( k \)-fold Cross-validation
    • -
  • The bias-variance tradeoff
    • -
  • Example code for Bias-Variance tradeoff
    • -
  • Understanding what happens
    • -
  • Summing up
    • -
  • Another Example from Scikit-Learn's Repository
    • -
  • More examples on bootstrap and cross-validation and errors
    • -
  • The same example but now with cross-validation
    • -
  • Cross-validation with Ridge
    • +
  • Bayes' Theorem and Ridge and Lasso Regression
    • +
  • Why resampling methods
    • +
  • Resampling methods
    • +
  • Resampling approaches can be computationally expensive
    • +
  • Why resampling methods ?
    • +
  • Statistical analysis
    • +
  • Resampling methods
    • +
  • Resampling methods: Jackknife and Bootstrap
    • +
  • Resampling methods: Jackknife
    • +
  • Jackknife code example
    • +
  • Resampling methods: Bootstrap
    • +
  • Resampling methods: Bootstrap background
    • +
  • Resampling methods: More Bootstrap background
    • +
  • Resampling methods: Bootstrap approach
    • +
  • Resampling methods: Bootstrap steps
    • +
  • Code example for the Bootstrap method
    • +
  • Various steps in cross-validation
    • +
  • How to set up the cross-validation for Ridge and/or Lasso
    • +
  • Cross-validation in brief
    • +
  • Code Example for Cross-validation and \( k \)-fold Cross-validation
    • +
  • The bias-variance tradeoff
    • +
  • Example code for Bias-Variance tradeoff
    • +
  • Understanding what happens
    • +
  • Summing up
    • +
  • Another Example from Scikit-Learn's Repository
    • +
  • More examples on bootstrap and cross-validation and errors
    • +
  • The same example but now with cross-validation
    • +
  • Cross-validation with Ridge
    • @@ -408,7 +413,7 @@ MathJax.Hub.Config({
  • 9
  • 10
  • ...
    • -
  • 71
    • +
  • 72
  • »
    • diff --git a/doc/pub/week36/html/week36-reveal.html b/doc/pub/week36/html/week36-reveal.html index a313e8b57..52e101281 100644 --- a/doc/pub/week36/html/week36-reveal.html +++ b/doc/pub/week36/html/week36-reveal.html @@ -1637,9 +1637,9 @@ Let us try to illustrate Bayes' theorem through an example.

    Example of Usage of Bayes' theorem

    -Let us suppose that you are undergoing a series of mammography scan in +Let us suppose that you are undergoing a series of mammography scans in order to rule out possible breast cancer cases. We define the -sensitivity for a positive event by the variable \( X \) (it takes binary +sensitivity for a positive event by the variable \( X \). It takes binary values with \( X=1 \) representing a positive event and \( X=0 \) being a negative event. We reserve \( Y \) as a classification parameter for either a negative or a postive breast cancer confirmation. @@ -1657,7 +1657,7 @@ $$

     

    -This obviously sounds scaring since many would conclude that if the test is positive, there is a likelihood of \( 80\% \) for having cancer. +This obviously sounds scary since many would conclude that if the test is positive, there is a likelihood of \( 80\% \) for having cancer. It is however not correct, as the following Bayesian analysis shows. @@ -1696,6 +1696,20 @@ That is, in case of a positive test, there is only a \( 3\% \) chance of having +

    +

    Bayes' Theorem and Ridge and Lasso Regression

    + +

    +Hitherto we have discussed Ridge and Lasso regression in terms of a +linear analysis. This may to many of you feel rather technical and +perhaps not that intuitive. The question is whether we can develop a +more intuitive way of understanding what Ridge and Lasso express. + +

    +Before we proceed let us perform a Ridge and OLS analysis of a polynomial fit. +

    + +

    Why resampling methods

    diff --git a/doc/pub/week36/html/week36-solarized.html b/doc/pub/week36/html/week36-solarized.html index d336592e8..5db8c9d00 100644 --- a/doc/pub/week36/html/week36-solarized.html +++ b/doc/pub/week36/html/week36-solarized.html @@ -175,6 +175,10 @@ div { text-align: justify; text-justify: inter-word; } None, 'example-of-usage-of-bayes-theorem'), ('Doing it correctly', 2, None, 'doing-it-correctly'), + ("Bayes' Theorem and Ridge and Lasso Regression", + 2, + None, + 'bayes-theorem-and-ridge-and-lasso-regression'), ('Why resampling methods', 2, None, 'why-resampling-methods'), ('Resampling methods', 2, None, 'resampling-methods'), ('Resampling approaches can be computationally expensive', @@ -1629,9 +1633,9 @@ Let us try to illustrate Bayes' theorem through an example.

    Example of Usage of Bayes' theorem

    -Let us suppose that you are undergoing a series of mammography scan in +Let us suppose that you are undergoing a series of mammography scans in order to rule out possible breast cancer cases. We define the -sensitivity for a positive event by the variable \( X \) (it takes binary +sensitivity for a positive event by the variable \( X \). It takes binary values with \( X=1 \) representing a positive event and \( X=0 \) being a negative event. We reserve \( Y \) as a classification parameter for either a negative or a postive breast cancer confirmation. @@ -1647,7 +1651,7 @@ p(X=1\vert Y=1) =0.8. $$

    -This obviously sounds scaring since many would conclude that if the test is positive, there is a likelihood of \( 80\% \) for having cancer. +This obviously sounds scary since many would conclude that if the test is positive, there is a likelihood of \( 80\% \) for having cancer. It is however not correct, as the following Bayesian analysis shows.

    @@ -1681,6 +1685,20 @@ That is, in case of a positive test, there is only a \( 3\% \) chance of having











    +

    Bayes' Theorem and Ridge and Lasso Regression

    + +

    +Hitherto we have discussed Ridge and Lasso regression in terms of a +linear analysis. This may to many of you feel rather technical and +perhaps not that intuitive. The question is whether we can develop a +more intuitive way of understanding what Ridge and Lasso express. + +

    +Before we proceed let us perform a Ridge and OLS analysis of a polynomial fit. + +

    +









    +

    Why resampling methods

    diff --git a/doc/pub/week36/html/week36.html b/doc/pub/week36/html/week36.html index ab2642584..1611b8ebe 100644 --- a/doc/pub/week36/html/week36.html +++ b/doc/pub/week36/html/week36.html @@ -180,6 +180,10 @@ div { text-align: justify; text-justify: inter-word; } None, 'example-of-usage-of-bayes-theorem'), ('Doing it correctly', 2, None, 'doing-it-correctly'), + ("Bayes' Theorem and Ridge and Lasso Regression", + 2, + None, + 'bayes-theorem-and-ridge-and-lasso-regression'), ('Why resampling methods', 2, None, 'why-resampling-methods'), ('Resampling methods', 2, None, 'resampling-methods'), ('Resampling approaches can be computationally expensive', @@ -1634,9 +1638,9 @@ Let us try to illustrate Bayes' theorem through an example.

    Example of Usage of Bayes' theorem

    -Let us suppose that you are undergoing a series of mammography scan in +Let us suppose that you are undergoing a series of mammography scans in order to rule out possible breast cancer cases. We define the -sensitivity for a positive event by the variable \( X \) (it takes binary +sensitivity for a positive event by the variable \( X \). It takes binary values with \( X=1 \) representing a positive event and \( X=0 \) being a negative event. We reserve \( Y \) as a classification parameter for either a negative or a postive breast cancer confirmation. @@ -1652,7 +1656,7 @@ p(X=1\vert Y=1) =0.8. $$

    -This obviously sounds scaring since many would conclude that if the test is positive, there is a likelihood of \( 80\% \) for having cancer. +This obviously sounds scary since many would conclude that if the test is positive, there is a likelihood of \( 80\% \) for having cancer. It is however not correct, as the following Bayesian analysis shows.

    @@ -1686,6 +1690,20 @@ That is, in case of a positive test, there is only a \( 3\% \) chance of having











    +

    Bayes' Theorem and Ridge and Lasso Regression

    + +

    +Hitherto we have discussed Ridge and Lasso regression in terms of a +linear analysis. This may to many of you feel rather technical and +perhaps not that intuitive. The question is whether we can develop a +more intuitive way of understanding what Ridge and Lasso express. + +

    +Before we proceed let us perform a Ridge and OLS analysis of a polynomial fit. + +

    +









    +

    Why resampling methods

    diff --git a/doc/pub/week36/ipynb/ipynb-week36-src.tar.gz b/doc/pub/week36/ipynb/ipynb-week36-src.tar.gz index 2298cfc20..816e723df 100644 Binary files a/doc/pub/week36/ipynb/ipynb-week36-src.tar.gz and b/doc/pub/week36/ipynb/ipynb-week36-src.tar.gz differ diff --git a/doc/pub/week36/ipynb/week36.ipynb b/doc/pub/week36/ipynb/week36.ipynb index 4f6aa65c4..a92f1e8a4 100644 --- a/doc/pub/week36/ipynb/week36.ipynb +++ b/doc/pub/week36/ipynb/week36.ipynb @@ -2052,9 +2052,9 @@ "\n", "## Example of Usage of Bayes' theorem\n", "\n", - "Let us suppose that you are undergoing a series of mammography scan in\n", + "Let us suppose that you are undergoing a series of mammography scans in\n", "order to rule out possible breast cancer cases. We define the\n", - "sensitivity for a positive event by the variable $X$ (it takes binary\n", + "sensitivity for a positive event by the variable $X$. It takes binary\n", "values with $X=1$ representing a positive event and $X=0$ being a\n", "negative event. We reserve $Y$ as a classification parameter for\n", "either a negative or a postive breast cancer confirmation.\n", @@ -2077,7 +2077,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This obviously sounds scaring since many would conclude that if the test is positive, there is a likelihood of $80\\%$ for having cancer.\n", + "This obviously sounds scary since many would conclude that if the test is positive, there is a likelihood of $80\\%$ for having cancer.\n", "It is however not correct, as the following Bayesian analysis shows.\n", "\n", "## Doing it correctly\n", @@ -2133,6 +2133,18 @@ "source": [ "That is, in case of a positive test, there is only a $3\\%$ chance of having cancer!\n", "\n", + "\n", + "## Bayes' Theorem and Ridge and Lasso Regression\n", + "\n", + "Hitherto we have discussed Ridge and Lasso regression in terms of a\n", + "linear analysis. This may to many of you feel rather technical and\n", + "perhaps not that intuitive. The question is whether we can develop a\n", + "more intuitive way of understanding what Ridge and Lasso express.\n", + "\n", + "Before we proceed let us perform a Ridge and OLS analysis of a polynomial fit. \n", + "\n", + "\n", + "\n", "## Why resampling methods\n", "\n", "Before we proceed, we need to rethink what we have been doing. In our\n", diff --git a/doc/src/week36/week36.do.txt b/doc/src/week36/week36.do.txt index 9ff0a78b6..7e9001b7d 100644 --- a/doc/src/week36/week36.do.txt +++ b/doc/src/week36/week36.do.txt @@ -1270,9 +1270,9 @@ Let us try to illustrate Bayes' theorem through an example. !split ===== Example of Usage of Bayes' theorem ===== -Let us suppose that you are undergoing a series of mammography scan in +Let us suppose that you are undergoing a series of mammography scans in order to rule out possible breast cancer cases. We define the -sensitivity for a positive event by the variable $X$ (it takes binary +sensitivity for a positive event by the variable $X$. It takes binary values with $X=1$ representing a positive event and $X=0$ being a negative event. We reserve $Y$ as a classification parameter for either a negative or a postive breast cancer confirmation. @@ -1287,7 +1287,7 @@ p(X=1\vert Y=1) =0.8. \] !et -This obviously sounds scaring since many would conclude that if the test is positive, there is a likelihood of $80\%$ for having cancer. +This obviously sounds scary since many would conclude that if the test is positive, there is a likelihood of $80\%$ for having cancer. It is however not correct, as the following Bayesian analysis shows. !split @@ -1318,6 +1318,19 @@ p(Y=1\vert X=1)=\frac{p(X=1\vert Y=1)p(Y=1)}{p(X=1\vert Y=1)p(Y=1)+p(X=1\vert Y= !et That is, in case of a positive test, there is only a $3\%$ chance of having cancer! + +!split +===== Bayes' Theorem and Ridge and Lasso Regression ===== + +Hitherto we have discussed Ridge and Lasso regression in terms of a +linear analysis. This may to many of you feel rather technical and +perhaps not that intuitive. The question is whether we can develop a +more intuitive way of understanding what Ridge and Lasso express. + +Before we proceed let us perform a Ridge and OLS analysis of a polynomial fit. + + + !split ===== Why resampling methods =====