updated README and index.md (#53)

README.md

@@ -1,5 +1,4 @@
-Bayesian Statistics with Julia and Turing
-================
+# Bayesian Statistics using Julia and Turing
 
 [![CC BY-SA
 4.0](https://img.shields.io/badge/License-CC%20BY--SA%204.0-lightgrey.svg)](http://creativecommons.org/licenses/by-sa/4.0/)
@@ -13,11 +12,19 @@ Bayesian for Everyone!
 
 </div>
 
-Welcome to the repository of tutorials on how to do **Bayesian Statistics** using [**Julia**](https://www.julialang.org) and [**Turing**](http://turing.ml/). Tutorials are available at [storopoli.github.io/Bayesian-Julia](https://storopoli.github.io/Bayesian-Julia).
+Welcome to the repository of tutorials on how to do **Bayesian Statistics** using [**Julia**](https://www.julialang.org) and [**Turing**](http://turing.ml/).
+Tutorials are available at [storopoli.github.io/Bayesian-Julia](https://storopoli.github.io/Bayesian-Julia).
 
-**Bayesian statistics** is an approach to inferential statistics based on Bayes' theorem, where available knowledge about parameters in a statistical model is updated with the information in observed data. The background knowledge is expressed as a prior distribution and combined with observational data in the form of a likelihood function to determine the posterior distribution. The posterior can also be used for making predictions about future events.
+**Bayesian statistics** is an approach to inferential statistics based on Bayes' theorem,
+where available knowledge about parameters in a statistical model is updated with the information in observed data.
+The background knowledge is expressed as a prior distribution and combined with observational data in the form of a likelihood function to determine the posterior distribution.
+The posterior can also be used for making predictions about future events.
 
-**Bayesian statistics** is a departure from classical inferential statistics that prohibits probability statements about parameters and is based on asymptotically sampling infinite samples from a theoretical population and finding parameter values that maximize the likelihood function. Mostly notorious is null-hypothesis significance testing (NHST) based on *p*-values. Bayesian statistics **incorporate uncertainty** (and prior knowledge) by allowing probability statements about parameters, and the process of parameter value inference is a direct result of the **Bayes' theorem**.
+**Bayesian statistics** is a departure from classical inferential statistics that prohibits probability statements about parameters and
+is based on asymptotically sampling infinite samples from a theoretical population and finding parameter values that maximize the likelihood function.
+Mostly notorious is null-hypothesis significance testing (NHST) based on *p*-values.
+Bayesian statistics **incorporate uncertainty** (and prior knowledge) by allowing probability statements about parameters,
+and the process of parameter value inference is a direct result of the **Bayes' theorem**.
 
 ## Table of Contents
 
@@ -37,7 +44,12 @@ Welcome to the repository of tutorials on how to do **Bayesian Statistics** usin
 
 ## Julia
 
-[**Julia**](https://www.julialang.org) is a fast dynamic-typed language that just-in-time (JIT) compiles into native code using LLVM. It ["runs like C but reads like Python"](https://www.nature.com/articles/d41586-019-02310-3), meaning that is *blazing* fast, easy to prototype and read/write code. It is multi-paradigm, combining features of imperative, functional, and object-oriented programming. I won't cover Julia basics and any sort of data manipulation using Julia in the tutorials, instead please take a look into the following resources which covers most of the introduction to Julia and how to work with tabular data in Julia:
+[**Julia**](https://www.julialang.org) is a fast dynamic-typed language that just-in-time (JIT) compiles into native code using LLVM.
+It ["runs like C but reads like Python"](https://www.nature.com/articles/d41586-019-02310-3),
+meaning that is *blazing* fast, easy to prototype and to read/write code.
+It is multi-paradigm, combining features of imperative, functional, and object-oriented programming.
+I won't cover Julia basics and any sort of data manipulation using Julia in the tutorials,
+instead please take a look into the following resources which covers most of the introduction to Julia and how to work with tabular data in Julia:
 
 * [**Julia Documentation**](https://docs.julialang.org/): Julia documentation is a very friendly and well-written resource that explains the basic design and functionality of the language.
 * [**Julia Data Science**](https://juliadatascience.io): open source and open access book on how to do Data Science using Julia.
@@ -47,15 +59,20 @@ Welcome to the repository of tutorials on how to do **Bayesian Statistics** usin
 
 ## Turing
 
-[**Turing**](http://turing.ml/) is an ecosystem of Julia packages for Bayesian Inference using [probabilistic programming](https://en.wikipedia.org/wiki/Probabilistic_programming). Models specified using Turing are easy to read and write — models work the way you write them. Like everything in Julia, Turing is [fast](https://arxiv.org/abs/2002.02702).
+[**Turing**](http://turing.ml/) is an ecosystem of Julia packages for Bayesian Inference using [probabilistic programming](https://en.wikipedia.org/wiki/Probabilistic_programming).
+Models specified using Turing are easy to read and write — models work the way you write them. Like everything in Julia, Turing is [fast](https://arxiv.org/abs/2002.02702).
 
 ## Author
 
 Jose Storopoli, PhD - [*Lattes* CV](http://lattes.cnpq.br/2281909649311607) - [ORCID](https://orcid.org/0000-0002-0559-5176) - <https://storopoli.io>
 
 ## How to use the content?
 
-The content is licensed under a very permissive Creative Commons license (CC BY-SA). You are mostly welcome to contribute with [issues](https://www.github.com/storopoli/Bayesian-Julia/issues) and [pull requests](https://github.com/storopoli/Bayesian-Julia/pulls). My hope is to have **more people into Bayesian statistics**. The content is aimed towards social scientists and PhD candidates in social sciences. I chose to provide an **intuitive approach** rather than focusing on rigorous mathematical formulations. I've made it to be how I would have liked to be introduced to Bayesian statistics.
+The content is licensed under a very permissive Creative Commons license (CC BY-SA).
+You are mostly welcome to contribute with [issues](https://www.github.com/storopoli/Bayesian-Julia/issues) and [pull requests](https://github.com/storopoli/Bayesian-Julia/pulls).
+My hope is to have **more people into Bayesian statistics**. The content is aimed towards social scientists and PhD candidates in social sciences.
+I chose to provide an **intuitive approach** rather than focusing on rigorous mathematical formulations.
+I've made it to be how I would have liked to be introduced to Bayesian statistics.
 
 To configure a local environment:
 
@@ -85,14 +102,40 @@ To configure a local environment:
 11. [**Computational Tricks with Turing (Non-Centered Parametrization and QR Decomposition)**](https://storopoli.github.io/Bayesian-Julia/pages/11_Turing_tricks/)
 12. [**Epidemiological Models using ODE Solvers in Turing**](https://storopoli.github.io/Bayesian-Julia/pages/12_epi_models/)
 
+## Datasets
+
+- `kidiq` (linear regression): data from a survey of adult American women and their children
+   (a subsample from the National Longitudinal Survey of Youth).
+   Source: Gelman and Hill (2007).
+- `wells` (logistic regression): a survey of 3200 residents in a small area of Bangladesh suffering
+   from arsenic contamination of groundwater.
+   Respondents with elevated arsenic levels in their wells had been encouraged to switch their water source
+   to a safe public or private well in the nearby area
+   and the survey was conducted several years later to
+   learn which of the affected residents had switched wells.
+   Souce: Gelman and Hill (2007).
+- `esoph` (ordinal regression): data from a case-control study of (o)esophageal cancer in Ille-et-Vilaine, France.
+   Source: Breslow and Day (1980).
+- `roaches` (Poisson regression): data on the efficacy of a pest management system at reducing the number of roaches in urban apartments.
+   Source: Gelman and Hill (2007).
+- `duncan` (robust regression): data from occupation's prestige filled with outliers.
+   Source: Duncan (1961).
+- `cheese` (hierarchical models): data from cheese ratings.
+   A group of 10 rural and 10 urban raters rated 4 types of different cheeses (A, B, C and D) in two samples.
+   Source: Boatwright, McCulloch and Rossi (1999).
+
 ## What about other Turing tutorials?
 
-Despite not being the only Turing tutorial that exists, this tutorial aims to introduce Bayesian inference along with how to use Julia and Turing. Here is a (not complete) list of other Turing tutorials:
+Despite not being the only Turing tutorial that exists, this tutorial aims to introduce Bayesian inference along with how to use Julia and Turing.
+Here is a (not complete) list of other Turing tutorials:
 
 1. [**Official Turing Tutorials**](https://turing.ml/dev/tutorials/): tutorials on how to implement common models in Turing
 2. [**Statistical Rethinking - Turing Models**](https://statisticalrethinkingjulia.github.io/TuringModels.jl/): Julia versions of the Bayesian models described in *Statistical Rethinking* Edition 1 (McElreath, 2016) and Edition 2 (McElreath, 2020)
 3. [**Håkan Kjellerstrand Turing Tutorials**](http://hakank.org/julia/turing/): a collection of Julia Turing models
 
+I also have a free and opensource graduate course on Bayesian Statistics with Turing and Stan code.
+You can find it at [`storopoli/Bayesian-Statistics`](https://github.com/storopoli/Bayesian-Statistics).
+
 ## How to cite
 
 To cite these tutorials, please use:
@@ -108,6 +151,10 @@ Or in BibTeX format (LaTeX):
       year = {2021}
     }
 
+## References
+
+The references are divided in **books**, **papers**, **software**, and **datasets**.
+
 ### Books
 
 * Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). *Bayesian Data Analysis*. Chapman and Hall/CRC.
@@ -126,17 +173,24 @@ Or in BibTeX format (LaTeX):
 * Amrhein, V., Greenland, S., & McShane, B. (2019). Scientists rise up against statistical significance. *Nature*, *567*(7748), 305–307. <https://doi.org/10.1038/d41586-019-00857-9>
 * van de Schoot, R., Kaplan, D., Denissen, J., Asendorpf, J. B., Neyer, F. J., & van Aken, M. A. G. (2014). A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research. *Child Development*, *85*(3), 842–860. <https://doi.org/10.1111/cdev.12169>
 
-### Software References
+### Software
 
 * Bezanson, J., Edelman, A., Karpinski, S., & Shah, V. B. (2017). Julia: A fresh approach to numerical computing. SIAM Review, 59(1), 65–98.
 * Ge, H., Xu, K., & Ghahramani, Z. (2018). Turing: A Language for Flexible Probabilistic Inference. International Conference on Artificial Intelligence and Statistics, 1682–1690. http://proceedings.mlr.press/v84/ge18b.html
 * Tarek, M., Xu, K., Trapp, M., Ge, H., & Ghahramani, Z. (2020). DynamicPPL: Stan-like Speed for Dynamic Probabilistic Models. ArXiv:2002.02702 [Cs, Stat]. http://arxiv.org/abs/2002.02702
 * Xu, K., Ge, H., Tebbutt, W., Tarek, M., Trapp, M., & Ghahramani, Z. (2020). AdvancedHMC.jl: A robust, modular and efficient implementation of advanced HMC algorithms. Symposium on Advances in Approximate Bayesian Inference, 1–10. http://proceedings.mlr.press/v118/xu20a.html
 * Revels, J., Lubin, M., & Papamarkou, T. (2016). Forward-Mode Automatic Differentiation in Julia. ArXiv:1607.07892 [Cs]. http://arxiv.org/abs/1607.07892
 
+### Datasets
+
+-   Boatwright, P., McCulloch, R., & Rossi, P. (1999). Account-level modeling for trade promotion: An application of a constrained parameter hierarchical model. _Journal of the American Statistical Association_, 94(448), 1063–1073.
+-   Breslow, N. E. & Day, N. E. (1980). **Statistical Methods in Cancer Research. Volume 1: The Analysis of Case-Control Studies**. IARC Lyon / Oxford University Press.
+-   Duncan, O. D. (1961). A socioeconomic index for all occupations. Class: Critical Concepts, 1, 388–426.
+-   Gelman, A., & Hill, J. (2007). **Data analysis using regression and
+    multilevel/hierarchical models**. Cambridge university press.
 
 ## License
 
 This content is licensed under [Creative Commons Attribution-ShareAlike 4.0 Internacional](http://creativecommons.org/licenses/by-sa/4.0/).
 
-[![CC BY-SA 4.0](https://licensebuttons.net/l/by-sa/4.0/88x31.png)](http://creativecommons.org/licenses/by-sa/4.0/)
+[![CC BY-SA 4.0](https://licensebuttons.net/l/by-sa/4.0/88x31.png)](http://creativecommons.org/licenses/by-sa/4.0/)