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update readme, minor edits
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‎06_issues.Rmd

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theta = c(theta0, rep(NA, nsim))
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for (t in 2:nsim) {
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thetaStar = rnorm(1, theta[-1], sd)
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thetaStar = rnorm(1, theta[t-1], sd)
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u = runif(1)
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r = exp(logPosterior_thetaStar - logPosterior_theta0)
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theta[t] = ifelse(u<=r, thetaStar, theta[-1])
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theta[t] = ifelse(u<=r, thetaStar, theta[t-1])
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}
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```
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‎LICENSE.md

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‎README.md

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# bayesian-basics
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# Bayesian Basics
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Raw files for a document that introduces Bayesian data analysis. While the focus is on concepts, demonstration is primarily via Stan, though BUGS, JAGS, and some raw R code is also available for those interested. [link to doc](https://m-clark.github.io/bayesian-basics/)
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This is a document that introduces Bayesian data analysis. It serves as a practical and applied introduction to Bayesian approaches for the uninitiated. The goal is to provide just enough information in a brief format to allow one to feel comfortable exploring Bayesian data analysis for themselves, assuming they have the requisite context to begin with.
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After a conceptual introduction, a fully visible by-hand example is provided using the binomial distribution. After that, the document proceeds to introduce fully Bayesian analysis with the standard linear regression model, as that is the basis for most applied statistics courses and is assumed to be most familiar to the reader. Model diagnostics, model enhancements, and additional modeling issues are then explored. Supplemental content in the appendix provides more technical detail if desired, and includes a maximum likelihood refresher, an overview of programming options in Bayesian analysis, the same regression model using BUGS and JAGS, and 'by-hand' code for the model using the Metropolis-Hastings and Hamiltonian Monte Carlo algorithms. [link to doc](https://m-clark.github.io/bayesian-basics/)
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Contents:
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- The Bayesian Idea
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- A by-hand example
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- A standard regression model
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- Diagnostics
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- Model enhancements
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- Common issues encountered
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- An appendix with some more detailed code exposition
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<img src="img/priorpost.png" style="display:block; margin: 0 auto;">
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There is a [shiny app to play with](https://micl.shinyapps.io/prior2post/) also.

‎docs/Bayesian-Basics.epub

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‎docs/a-hands-on-example.html

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‎docs/appendix.html

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‎docs/index.html

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<h4 class="author"><em><div class="title">
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<span style="font-size:150%; font-variant:small-caps; font-style:normal; font-family:&#39;Roboto&#39;">Michael Clark</span><br><br> <img src="img/signature-acronym.png" style="width:30%; padding:10px 0;"> <br> <img src="img/ARC-acronym-signature.png" style="width:21%; padding:10px 0;">
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</div></em></h4>
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<h4 class="date"><em>2018-05-11</em></h4>
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<h4 class="date"><em>2018-05-17</em></h4>
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</div>
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<div id="section" class="section level1">
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<h1></h1>

‎docs/introduction.html

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‎docs/issues.html

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theta =<span class="st"> </span><span class="kw">c</span>(theta0, <span class="kw">rep</span>(<span class="ot">NA</span>, nsim))
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<span class="cf">for</span> (t <span class="cf">in</span> <span class="dv">2</span><span class="op">:</span>nsim) {
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thetaStar =<span class="st"> </span><span class="kw">rnorm</span>(<span class="dv">1</span>, theta[<span class="op">-</span><span class="dv">1</span>], sd)
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thetaStar =<span class="st"> </span><span class="kw">rnorm</span>(<span class="dv">1</span>, theta[t<span class="op">-</span><span class="dv">1</span>], sd)
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u =<span class="st"> </span><span class="kw">runif</span>(<span class="dv">1</span>)
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r =<span class="st"> </span><span class="kw">exp</span>(logPosterior_thetaStar <span class="op">-</span><span class="st"> </span>logPosterior_theta0)
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theta[t] =<span class="st"> </span><span class="kw">ifelse</span>(u<span class="op">&lt;=</span>r, thetaStar, theta[<span class="op">-</span><span class="dv">1</span>])
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theta[t] =<span class="st"> </span><span class="kw">ifelse</span>(u<span class="op">&lt;=</span>r, thetaStar, theta[t<span class="op">-</span><span class="dv">1</span>])
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}</code></pre></div>
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<p>One can see the <a href="appendix.html#metropolis-hastings-example">Metropolis-Hastings Example</a> to see the Metropolis algorithm applied to our regression problem.</p>
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‎docs/model-enhancements.html

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‎docs/model-exploration.html

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‎docs/preface.html

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‎docs/regression-models.html

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‎img/priorpost.png

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‎packages.bib

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year = {2018},
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url = {https://www.R-project.org/},
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}
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@Manual{R-bbmle,
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title = {bbmle: Tools for General Maximum Likelihood Estimation},
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author = {Ben Bolker and R Development Core Team},
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year = {2017},
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note = {R package version 1.0.20},
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url = {https://CRAN.R-project.org/package=bbmle},
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}
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@Manual{R-bindrcpp,
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title = {bindrcpp: An 'Rcpp' Interface to Active Bindings},
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author = {Kirill Müller},
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year = {2018},
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note = {R package version 0.2.2},
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url = {https://CRAN.R-project.org/package=bindrcpp},
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}
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@Manual{R-bookdown,
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title = {bookdown: Authoring Books and Technical Documents with R Markdown},
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author = {Yihui Xie},
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year = {2018},
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note = {R package version 0.7},
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url = {https://CRAN.R-project.org/package=bookdown},
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}
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@Manual{R-coda,
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title = {coda: Output Analysis and Diagnostics for MCMC},
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author = {Martyn Plummer and Nicky Best and Kate Cowles and Karen Vines and Deepayan Sarkar and Douglas Bates and Russell Almond and Arni Magnusson},
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year = {2016},
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note = {R package version 0.19-1},
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url = {https://CRAN.R-project.org/package=coda},
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}
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@Manual{R-dplyr,
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title = {dplyr: A Grammar of Data Manipulation},
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url = {https://CRAN.R-project.org/package=rmarkdown},
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}
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@Manual{R-rstan,
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title = {rstan: R Interface to Stan},
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author = {Jiqiang Guo and Jonah Gabry and Ben Goodrich},
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year = {2018},
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note = {R package version 2.17.3},
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url = {https://CRAN.R-project.org/package=rstan},
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}
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@Manual{R-StanHeaders,
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title = {StanHeaders: C++ Header Files for Stan},
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author = {Ben Goodrich and Andrew Gelman and Bob Carpenter and Matt Hoffman and Daniel Lee and Michael Betancourt and Marcus Brubaker and Jiqiang Guo and Peter Li and Allen Riddell and Marco Inacio and Mitzi Morris and Jeffrey Arnold and Rob Goedman and Brian Lau and Rob Trangucci and Jonah Gabry and Alp Kucukelbir and Robert Grant and Dustin Tran and Michael Malecki and Yuanjun Gao},
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year = {2018},
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note = {R package version 2.17.2},
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url = {https://CRAN.R-project.org/package=StanHeaders},
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}
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@Manual{R-stringr,
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title = {stringr: Simple, Consistent Wrappers for Common String Operations},
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author = {Hadley Wickham},

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