From 3a313d8c966ae03bce36b59d19c835d1705dbeca Mon Sep 17 00:00:00 2001 From: Josh Cook Date: Thu, 2 Dec 2021 06:36:58 -0500 Subject: [PATCH 1/4] chore: setup section 12 --- _site.yml | 2 + index.Rmd | 1 + notes/12_extended-topics.Rmd | 28 + notes/12_extended-topics.html | 2533 +++++++++++++++++++++++++++++++++ slides/slides_extra.pdf | Bin 0 -> 1543517 bytes 5 files changed, 2564 insertions(+) create mode 100644 notes/12_extended-topics.Rmd create mode 100644 notes/12_extended-topics.html create mode 100644 slides/slides_extra.pdf diff --git a/_site.yml b/_site.yml index 2c5bfcb..ea51d26 100644 --- a/_site.yml +++ b/_site.yml @@ -37,6 +37,8 @@ navbar: href: notes/10_decision-analysis_bda3-9.html - text: "Section 11. Normal approximation & Frequency properties" href: notes/11_normal-approx-freq-properties_bda3-04.html + - text: "Section 12. Extended topics" + href: notes/12_extended-topics.html - text: "Exercises" menu: - text: "Chapter 1" diff --git a/index.Rmd b/index.Rmd index 5c2b0c9..cc006c3 100644 --- a/index.Rmd +++ b/index.Rmd @@ -54,6 +54,7 @@ The recommended way to go through the material is: | **9. Model comparison and selection** | [notes](notes/09_model-selection_bda3-7.html) | (none) | [assignment 8](assignments/jhcook-assignment-08.html) | | **10. Decision analysis** | [notes](notes/10_decision-analysis_bda3-9.html) | (none) | [assignment 9](assignments/jhcook-assignment-09.html) | | **11. Normal approximation & Frequency properties** | [notes](notes/11_normal-approx-freq-properties_bda3-04.html) | (none) | (none) | +| **12. Extended topics** | [notes](notes/12_extended-topics.html) | (none) | (none) | ## Stan models diff --git a/notes/12_extended-topics.Rmd b/notes/12_extended-topics.Rmd new file mode 100644 index 0000000..db858f5 --- /dev/null +++ b/notes/12_extended-topics.Rmd @@ -0,0 +1,28 @@ +--- +title: "00. Title" +date: "2021-10-01" +output: distill::distill_article +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set(echo = TRUE, dpi = 300, comment = "#>") +``` + +## Resources + +- reading: + - end of BDA3 ch. 4 + - optional: BDA3 ch. 8, 14-18, 21 +- lectures: + - ['12.1 Frequency evaluation, hypothesis testing and variable selection'](https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=e998b5dd-bf8e-42da-9f7c-ab1700ca2702) + - ['12.2 Overview of modeling data collection, BDA3 Ch 8, linear models, BDA Ch 14-18, lasso, horseshoe and Gaussian processes, BDA3 Ch 21'](https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=e998b5dd-bf8e-42da-9f7c-ab1700ca2702) +- [slides](../slides/slides_extra.pdf) + +## Notes + +### Lecture 12.1 Frequency evaluation, hypothesis testing and variable selection + + + + +### Lecture 12.2 Overview of modeling data collection, BDA3 Ch 8, linear models, BDA Ch 14-18, lasso, horseshoe and Gaussian processes, BDA3 Ch 21 diff --git a/notes/12_extended-topics.html b/notes/12_extended-topics.html new file mode 100644 index 0000000..4e2f1ce --- /dev/null +++ b/notes/12_extended-topics.html @@ -0,0 +1,2533 @@ + + + + + + + + + + + + + + + + + + + + 00. Title + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+

00. Title

+ + + +
+ + +
+

Resources

+ +

Notes

+

Reading instructions

+ +

Chapter N. Chapter title

+ +

Lecture notes

+
+ + +
+ +
+
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This article is in review.

@@ -2479,7 +2479,7 @@

This article is in review.

-

00. Title

+

12. Extended topics

@@ -2502,15 +2502,73 @@

Resources

  • slides
  • Notes

    -

    Reading instructions

    +

    Lecture 12.1 Frequency evaluation, hypothesis testing and variable selection

      -
    • notes from the reading instructions
    • -
    -

    Chapter N. Chapter title

    +
  • Bayesian vs. Frequentist +
      +
    • Bayesian theory has epistemic and aleatory probabilities
    • +
    • Frequency evaluations focus on frequency properties given aleatoric repetition of an observation and modeling
    • +
  • +
  • on “null hypothesis testing”: +
      +
    • often inappropriate to test the probability that a value is 0 +
        +
      • for continuous data, the probability of a single value is always 0
      • +
      • “region of practical equivalence” (ROPE) is another option
      • +
    • +
    • best to focus on describing the full posterior
        -
      • notes from the book
      • +
      • e.g. amount of the posterior greater than or less than an important value
      • +
      • e.g. where most of the posterior density is (89% or 95% HDI)
      • +
    • +
  • +
  • be careful about only looking at marginal posteriors, too +
      +
    • joint posterior distributions may be informative
    • +
    • e.g. height and weight variables in beta-blocker model are highly correlated; both marginals overlap 0, but joint does not
    • +
  • +
  • most common statistical tests are linear models +
  • -

    Lecture notes

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    classical testBayesian equivalentin ‘rstanarm’
    t-testmean of datastan_glm(y ~ 1)
    paired t-testmean of diffsstan_glm((y1 - y2) ~ 1)
    Pearson correlationlinear modelstan_glm(y ~ 1 + x)
    two-sample t-testgroup meansstan_glm(y ~ 1 + gid)
    ANOVAhierarchical modelstan_glm(y ~ 1 + (1|gid))
    +

    Lecture 12.2 Overview of modeling data collection, BDA3 Ch 8, linear models, BDA Ch 14-18, lasso, horseshoe and Gaussian processes, BDA3 Ch 21

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    Resources

  • lectures:
  • slides
  • @@ -2569,6 +2569,19 @@

    Lecture 12.2 Overview of modeling data collection, BDA3 Ch 8, linear models, BDA Ch 14-18, lasso, horseshoe and Gaussian processes, BDA3 Ch 21

    +
      +
    • LASSO and Bayesian LASSO +
        +
      • Bayesian LASSO uses Laplace distribution as a prior
      • +
      • is equivalent to L1 penalty in MLE LASSO, but because we still integrate over the entire posterior, it does not have the same “sparsifying” effect
      • +
      • therefore, Bayesian LASSO is empirically worse than MLE LASSO
      • +
      • final thought: best to separate the process of prior selection, posterior inference, and decision analysis
      • +
      • regularized horseshoe prior a better choice if you have prior information that only some of the covariates are informative
      • +
    • +
    +
    +projpred selection vs LASSO +
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1 + docs/search.json | 8 +- docs/sitemap.xml | 4 +- docs/slides/slides_extra.pdf | Bin 0 -> 2559163 bytes 9 files changed, 2677 insertions(+), 6 deletions(-) create mode 100644 docs/notes/12_extended-topics.Rmd create mode 100644 docs/notes/12_extended-topics.html create mode 100644 docs/notes/assets/12_extended-topics/slides-extra_s23.jpg create mode 100644 docs/slides/slides_extra.pdf diff --git a/docs/about.html b/docs/about.html index 8ced4e7..f267d24 100644 --- a/docs/about.html +++ b/docs/about.html @@ -2395,6 +2395,7 @@

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    Section 9. Model comparison and selection Section 10. Decision analysis Section 11. Normal approximation & Frequency properties +Section 12. Extended topics

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z7bN!K@eYL0g2k-@6R*pq0-BMAGqgqp|rd6oQGM`hPT!XEf`#u6e19OpEbK$*m(XXKk0dU3` z*Q{uL2vNPCqxu|{ps{Q4u2a`O9TbPW5^+J-=S+&d<*cB?8$+RqUc0Mp<;4eLKZ0;! zJ%}UuV Date: Fri, 3 Dec 2021 07:05:29 -0500 Subject: [PATCH 3/4] notes: lecture 12.2 --- notes/12_extended-topics.Rmd | 11 ++++++++++- notes/12_extended-topics.html | 15 ++++++++++++++- .../12_extended-topics/slides-extra_s23.jpg | Bin 0 -> 186146 bytes 3 files changed, 24 insertions(+), 2 deletions(-) create mode 100644 notes/assets/12_extended-topics/slides-extra_s23.jpg diff --git a/notes/12_extended-topics.Rmd b/notes/12_extended-topics.Rmd index 497ff37..aa10b6c 100644 --- a/notes/12_extended-topics.Rmd +++ b/notes/12_extended-topics.Rmd @@ -15,7 +15,7 @@ knitr::opts_chunk$set(echo = TRUE, dpi = 300, comment = "#>") - optional: BDA3 ch. 8, 14-18, 21 - lectures: - ['12.1 Frequency evaluation, hypothesis testing and variable selection'](https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=e998b5dd-bf8e-42da-9f7c-ab1700ca2702) - - ['12.2 Overview of modeling data collection, BDA3 Ch 8, linear models, BDA Ch 14-18, lasso, horseshoe and Gaussian processes, BDA3 Ch 21'](https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=e998b5dd-bf8e-42da-9f7c-ab1700ca2702) + - ['12.2 Overview of modeling data collection, BDA3 Ch 8, linear models, BDA Ch 14-18, lasso, horseshoe and Gaussian processes, BDA3 Ch 21'](https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=c43c862a-a5a4-45da-9b27-ab1700e12012) - [slides](../slides/slides_extra.pdf) ## Notes @@ -47,3 +47,12 @@ knitr::opts_chunk$set(echo = TRUE, dpi = 300, comment = "#>") | ANOVA | hierarchical model | `stan_glm(y ~ 1 + (1|gid))` | ### Lecture 12.2 Overview of modeling data collection, BDA3 Ch 8, linear models, BDA Ch 14-18, lasso, horseshoe and Gaussian processes, BDA3 Ch 21 + +- LASSO and Bayesian LASSO + - Bayesian LASSO uses Laplace distribution as a prior + - is equivalent to L1 penalty in MLE LASSO, but because we still integrate over the entire posterior, it does not have the same "sparsifying" effect + - therefore, Bayesian LASSO is empirically worse than MLE LASSO + - final thought: best to separate the process of prior selection, posterior inference, and decision analysis + - **regularized horseshoe prior** a better choice if you have prior information that only some of the covariates are informative + +![projpred selection vs LASSO](assets/12_extended-topics/slides-extra_s23.jpg) diff --git a/notes/12_extended-topics.html b/notes/12_extended-topics.html index da2a263..51b416f 100644 --- a/notes/12_extended-topics.html +++ b/notes/12_extended-topics.html @@ -2497,7 +2497,7 @@

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z7bN!K@eYL0g2k-@6R*pq0-BMAGqgqp|rd6oQGM`hPT!XEf`#u6e19OpEbK$*m(XXKk0dU3` z*Q{uL2vNPCqxu|{ps{Q4u2a`O9TbPW5^+J-=S+&d<*cB?8$+RqUc0Mp<;4eLKZ0;! zJ%}UuV Date: Thu, 2 Dec 2021 07:31:32 -0500 Subject: [PATCH 2/4] notes: lecture 12.1 --- notes/12_extended-topics.Rmd | 29 ++++++++++-- notes/12_extended-topics.html | 86 ++++++++++++++++++++++++++++------ slides/slides_extra.pdf | Bin 1543517 -> 2559163 bytes 3 files changed, 97 insertions(+), 18 deletions(-) diff --git a/notes/12_extended-topics.Rmd b/notes/12_extended-topics.Rmd index db858f5..497ff37 100644 --- a/notes/12_extended-topics.Rmd +++ b/notes/12_extended-topics.Rmd @@ -1,6 +1,6 @@ --- -title: "00. Title" -date: "2021-10-01" +title: "12. Extended topics" +date: "2021-12-02" output: distill::distill_article --- @@ -22,7 +22,28 @@ knitr::opts_chunk$set(echo = TRUE, dpi = 300, comment = "#>") ### Lecture 12.1 Frequency evaluation, hypothesis testing and variable selection - - +- Bayesian vs. Frequentist + - Bayesian theory has epistemic and aleatory probabilities + - Frequency evaluations focus on frequency properties given aleatoric repetition of an observation and modeling +- on "null hypothesis testing": + - often inappropriate to test the probability that a value is 0 + - for continuous data, the probability of a single value is always 0 + - "region of practical equivalence" (ROPE) is another option + - best to focus on describing the full posterior + - e.g. amount of the posterior greater than or less than an important value + - e.g. where most of the posterior density is (89% or 95% HDI) +- be careful about only looking at marginal posteriors, too + - joint posterior distributions may be informative + - e.g. height and weight variables in beta-blocker model are highly correlated; both marginals overlap 0, but joint does not +- most common statistical tests are linear models + - longer list with more illustrations: https://lindeloev.github.io/tests-as-linear + +| classical test | Bayesian equivalent | in 'rstanarm' | +|---------------------|---------------------|-----------------------------| +| t-test | mean of data | `stan_glm(y ~ 1)` | +| paired t-test | mean of diffs | `stan_glm((y1 - y2) ~ 1)` | +| Pearson correlation | linear model | `stan_glm(y ~ 1 + x)` | +| two-sample t-test | group means | `stan_glm(y ~ 1 + gid)` | +| ANOVA | hierarchical model | `stan_glm(y ~ 1 + (1|gid))` | ### Lecture 12.2 Overview of modeling data collection, BDA3 Ch 8, linear models, BDA Ch 14-18, lasso, horseshoe and Gaussian processes, BDA3 Ch 21 diff --git a/notes/12_extended-topics.html b/notes/12_extended-topics.html index 4e2f1ce..da2a263 100644 --- a/notes/12_extended-topics.html +++ b/notes/12_extended-topics.html @@ -86,28 +86,28 @@ - 00. Title + 12. Extended topics - - + + - + - + @@ -2469,7 +2469,7 @@