#13 from jhrcook/section-12

Section 12

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         - 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"

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 <a href="notes/09_model-selection_bda3-7.html">Section 9. Model comparison and selection</a>
 <a href="notes/10_decision-analysis_bda3-9.html">Section 10. Decision analysis</a>
 <a href="notes/11_normal-approx-freq-properties_bda3-04.html">Section 11. Normal approximation &amp; Frequency properties</a>
+<a href="notes/12_extended-topics.html">Section 12. Extended topics</a>
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 <a href="notes/09_model-selection_bda3-7.html">Section 9. Model comparison and selection</a>
 <a href="notes/10_decision-analysis_bda3-9.html">Section 10. Decision analysis</a>
 <a href="notes/11_normal-approx-freq-properties_bda3-04.html">Section 11. Normal approximation &amp; Frequency properties</a>
+<a href="notes/12_extended-topics.html">Section 12. Extended topics</a>
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 <td>(none)</td>
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+<tr class="even">
+<td><strong>12. Extended topics</strong></td>
+<td><a href="notes/12_extended-topics.html">notes</a></td>
+<td>(none)</td>
+<td>(none)</td>
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 <h2 id="stan-models">Stan models</h2>

docs/notes/12_extended-topics.Rmd

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+---
+title: "12. Extended topics"
+date: "2021-12-02"
+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=c43c862a-a5a4-45da-9b27-ab1700e12012)
+- [slides](../slides/slides_extra.pdf)
+
+## Notes
+
+### 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
+
+- 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)