class: center, middle, inverse, title-slide # Teaching and Learning Bayesian Statistics with {bayesrules} ## <a href="https://bit.ly/dogucu-talks">bit.ly/dogucu-talks</a> ### Mine Dogucu ### 2021-07-08 --- class: middle center <img src="img/headshot.jpeg" alt="A headshot of a woman with curly, short, ear-length hair with green eyes and red lipstick." style="width:165px; margin-top:20px; border: 3px solid whitesmoke; padding: 10px;"> .large[<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg>] <a href = "http://twitter.com/MineDogucu">MineDogucu</a> .large[<svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>] <a href = "http://github.com/mdogucu">mdogucu</a> .large[<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg>] <a href = "http://minedogucu.com">minedogucu.com</a> --- class: middle .pull-left[ .center[ <img src="img/alicia.jpg" alt="A headshot of a woman with long blonde hair wearing a brownish yellow tshirt and a red and pink floral silk scarf wrapped around her neck." style="width:165px; margin-top:20px; border: 3px solid whitesmoke; padding: 10px;"> Alicia Johnson .font-20[Macalester College] [<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg>](https://ajohns24.github.io/portfolio) [<svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>](https://github.com/ajohns24) ] ] .pull-right[ .center[ <img src="img/miles.png" alt="A headshot of a man with short dark hair, and a dark moustache. He is wearing a blue button up shirt and dark gray jacket" style="width:165px; margin-top:20px; border: 3px solid whitesmoke; padding: 10px;"> Miles Ott .font-20[Smith College] [<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg>](https://milesott.com/) [<svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>](https://github.com/MilesOtt) [<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg>](https://twitter.com/Miles_Ott) ] ] --- class:center <img src="img/bayes-rules-hex.png" title="a hex shaped logo with shiny green-pink disco ball and purple starry background. There is text that says Bayes Rules!" alt="a hex shaped logo with shiny green-pink disco ball and purple starry background. There is text that says Bayes Rules!" width="25%" style="display: block; margin: auto;" /> .pull-left[ <script src="https://use.fontawesome.com/releases/v5.15.1/js/all.js" data-auto-replace-svg="nest"></script> <i class="fas fa-book fa-2x" aria-hidden="true" title="Book icon"></i> [Bayes Rules! An Introduction to Bayesian Modeling with R](https://bayesrulesbook.com) ] .pull-right[ <i class="fab fa-r-project fa-2x" aria-hidden="true" title="R logo"></i> [{bayesrules}](https://www.github.com/bayes-rules/bayesrules) ] --- class: center middle ### Who are you? .pull-left[ <img src="img/teacher.png" title="an illustration of a woman holding a book standing in front of a blackboard" alt="an illustration of a woman holding a book standing in front of a blackboard" width="70%" style="display: block; margin: auto;" /> ] -- .pull-right[ <img src="img/student-solo.png" title="an illustration of a heafshot of a man with glasses and a tie with a shirt collar" alt="an illustration of a heafshot of a man with glasses and a tie with a shirt collar" width="40%" style="display: block; margin: auto;" /> ] --- class: middle ### A quick example Let `\(\pi\)` be the proportion of spam emails where `\(\pi \in [0, 1]\)`. -- What do you think `\(\pi\)` is? How certain are you? --- ## Binomial Likelihood ```r plot_binomial_likelihood(y = 3, n = 10) ``` <img src="index_files/figure-html/unnamed-chunk-5-1.png" title="X axis reads pi with values from 0 to 1. Y axis reads l of pi given capital Y = y). The curve of the graph has a high peak on the y-axis when pi equals to 0.3. The y-values are almost zero when pi is greater than 0.75." alt="X axis reads pi with values from 0 to 1. Y axis reads l of pi given capital Y = y). The curve of the graph has a high peak on the y-axis when pi equals to 0.3. The y-values are almost zero when pi is greater than 0.75." style="display: block; margin: auto;" /> --- ## Prior Model .pull-left[ ```r plot_beta(alpha = 4, beta = 4) ``` <img src="index_files/figure-html/unnamed-chunk-6-1.png" title="X axis reads pi with values from 0 to 1. Y axis reads f of pi). The curve of the graph has a high peak on the y-axis when pi equals to 0.5. The distribution is symmentric." alt="X axis reads pi with values from 0 to 1. Y axis reads f of pi). The curve of the graph has a high peak on the y-axis when pi equals to 0.5. The distribution is symmentric." style="display: block; margin: auto;" /> ] .pull-right[ ```r plot_beta(alpha = 1, beta = 10) ``` <img src="index_files/figure-html/unnamed-chunk-7-1.png" title="X axis reads pi with values from 0 to 1. Y axis reads f of pi). The curve of the graph has a high peak on the y-axis when pi equals to 0. The curve is a concave one and y is decreasing as pi is increasing." alt="X axis reads pi with values from 0 to 1. Y axis reads f of pi). The curve of the graph has a high peak on the y-axis when pi equals to 0. The curve is a concave one and y is decreasing as pi is increasing." style="display: block; margin: auto;" /> ] --- ## Posterior Model ```r plot_beta_binomial(alpha = 1, beta = 10, y = 3, n = 10) ``` <img src="index_files/figure-html/unnamed-chunk-8-1.png" title="X axis reads pi with values from 0 to 1. Y axis reads density. Three curves are shown labeled as prior, (scaled) likelihood, and posterior. The prior curve of the graph has a high peak on the y-axis when pi equals to 0. The curve is a concave one and y is decreasing as pi is increasing. The likelihood curve has a high peak on the y-axis when pi equals to 0.3. The y-values are almost zero when pi is greater than 0.75. The posterior sits between the prior and likelihood curves." alt="X axis reads pi with values from 0 to 1. Y axis reads density. Three curves are shown labeled as prior, (scaled) likelihood, and posterior. The prior curve of the graph has a high peak on the y-axis when pi equals to 0. The curve is a concave one and y is decreasing as pi is increasing. The likelihood curve has a high peak on the y-axis when pi equals to 0.3. The y-values are almost zero when pi is greater than 0.75. The posterior sits between the prior and likelihood curves." style="display: block; margin: auto;" /> --- class: middle ### Target Audience of the Book .pull-left[ <img src="img/student.png" title="an illustration of four students with bags who are holding workbooks." alt="an illustration of four students with bags who are holding workbooks." width="100%" style="display: block; margin: auto;" /> ] .pull-right[ - Advanced Undergraduate Students in Statistics / Data Science Programs - Equally trained learners - Prior course/training in statistics is required - Familiarity with probability, calculus, and tidyverse is recommended. ] --- class: middle ## Our Motivation - Bayesian methods are becoming more popular due to computing advances and reevaluation of subjectivity. - Lack of resources for the target audience. --- class: middle <style type="text/css"> .panelset { --panel-tab-foreground: whitesmoke; --panel-tab-active-foreground: whitesmoke; --panel-tabs-border-bottom: #00a1a1; --panel-tab-inactive-opacity: 0.5;} </style> .panelset.sideways[ .panel[.panel-name[Unit 1] ### Bayesian Foundations .pull-right[ - Bayes' Rule - The Beta-Binomial Bayesian Model - Balance and Sequentiality in Bayesian Analysis - Conjugate Families ] .pull-left[ <img src="index_files/figure-html/unnamed-chunk-11-1.png" title="three curves on a single plot with no axis labeled. It is coloring scheme indicates its similarity to the previous plot with prior, scaled likelihood and posterior" alt="three curves on a single plot with no axis labeled. It is coloring scheme indicates its similarity to the previous plot with prior, scaled likelihood and posterior" style="display: block; margin: auto;" /> ] ] .panel[.panel-name[Unit 2] ### Posterior Simulation & Analysis .pull-right[ <img src="img/unit2.png" title="A traceplot with no axis labels. Traceplots have thin vertical lines with varying lengths." alt="A traceplot with no axis labels. Traceplots have thin vertical lines with varying lengths." width="100%" style="display: block; margin: auto;" /> ] .pull-left[ - Grid Approximation - The Metropolis-Hastings Algorithm - Posterior Estimation - Posterior Hypothesis Testing - Posterior Prediction ] ] .panel[.panel-name[Unit 3] ### Regression and Classification .pull-right[ <img src="img/unit3.png" title="A scatterplot with multiple regression lines passing through points. These regression lines are not all over the place, they are clustered with similar but varyin intercepts and slopes." alt="A scatterplot with multiple regression lines passing through points. These regression lines are not all over the place, they are clustered with similar but varyin intercepts and slopes." width="100%" style="display: block; margin: auto;" /> ] .pull-left[ - Normal Regression - Poisson and Negative Binomial Regression - Logistic Regression - Naive Bayes Classification ] ] .panel[.panel-name[Unit 4] ### Hierarchical Models .pull-right[ <img src="img/unit4.png" title="a figure showing hierarchy with a rectangle on top. With a set of arrows pointing downwards leading to a set of rectangles below which also have a set of arrows pointing downwards leading to a different set of rectangles." alt="a figure showing hierarchy with a rectangle on top. With a set of arrows pointing downwards leading to a set of rectangles below which also have a set of arrows pointing downwards leading to a different set of rectangles." width="100%" style="display: block; margin: auto;" /> ] .pull-left[ - Normal hierarchical models without predictors - Normal hierarchical models with predictors - Non-Normal Hierarchical Regression & Classification ] ] ] --- class: center middle .large[Pedagogical Approach] --- class: middle center ## Checking Intuition <img src="img/fake-news-diagram.png" title="There are two ellipses at the top of the image. The first ellipse reads 'Prior: Only 40% of articles are fake'. The second ellipse reads 'Data: Exclamation points are more common among fake news'. There are two arrows each from the upper two ellipses leading to a third ellipse in the lower part of the image. The third ellipse reads 'Posterior: Is the article fake or not?'" alt="There are two ellipses at the top of the image. The first ellipse reads 'Prior: Only 40% of articles are fake'. The second ellipse reads 'Data: Exclamation points are more common among fake news'. There are two arrows each from the upper two ellipses leading to a third ellipse in the lower part of the image. The third ellipse reads 'Posterior: Is the article fake or not?'" width="80%" style="display: block; margin: auto;" /> --- .center[ ## Active Learning .pull-left[ Quizzes [Quiz Yourself](https://www.bayesrulesbook.com/chapter-1.html#quiz-yourself-1) <img src="img/quiz.png" title="An icon with a question mark and for choices labeled as A, B, C, and D." alt="An icon with a question mark and for choices labeled as A, B, C, and D." width="40%" style="display: block; margin: auto;" /> ] .pull-right[ Hands-on Programming [Metropolis-Hastings Algorithm](https://www.bayesrulesbook.com/chapter-7.html#the-metropolis-hastings-algorithm) <img src="img/programming.png" title="An icon of a student sitting on a chair and in front a desk with a computer typing." alt="An icon of a student sitting on a chair and in front a desk with a computer typing." width="40%" style="display: block; margin: auto;" /> ] ] --- class: center middle ### Computing and Math Together .pull-left[ <i class="fas fa-laptop-code fa-6x" aria-hidden="true" title="Laptop icon with code"></i> ] <i class="fas fa-subscript fa-6x" aria-hidden="true" title="X sub 1"></i> --- class: middle center .pull-left[ ### Compute for a Single Case <img src="img/build.png" title="A construction sign with a figure shoveling." alt="A construction sign with a figure shoveling." width="50%" style="display: block; margin: auto;" /> ] .pull-right[ ### Then Use Built-In Functions <i class="fab fa-r-project fa-7x" aria-hidden="true" title="R logo"></i> ] --- class: center middle ## Accessibility and Inclusion .pull-left[ <i class="fas fa-lock-open fa-6x" aria-hidden="true" title="open lock"></i> .footnote[More on the topic is available on [DataPedagogy blog](https://www.datapedagogy.com/#category:Bayes_Rules!_book)] <i class="fas fa-pen fa-6x" aria-hidden="true" title="pen"></i> ] .pull-right[ <i class="fas fa-blind fa-6x" aria-hidden="true" title="open lock"></i> <i class="fas fa-table fa-6x" aria-hidden="true" title="table"></i> ] --- class: center middle .font-75[R packages] --- class: middle center .large[<svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>] <a href = "http://github.com/bayes-rules/bayesrules">library(bayesrules)</a> ```r devtools::install_github("bayes-rules/bayesrules") ``` --- .pull-left[ ```r plot_beta(alpha = 3, beta = 8) ``` <div class="figure" style="text-align: center"> <img src="index_files/figure-html/unnamed-chunk-20-1.png" alt="X axis reads pi with values from 0 to 1. Y axis reads f of pi). The curve of the graph has a high peak on the y-axis when pi equals to 0.25. The y-values are almost zero when pi is greater than 0.70." /> <p class="caption">X axis reads pi with values from 0 to 1. Y axis reads f of pi). The curve of the graph has a high peak on the y-axis when pi equals to 0.25. The y-values are almost zero when pi is greater than 0.70.</p> </div> ] .pull-right[ ```r plot_beta(alpha = 10, beta = 2) ``` <div class="figure" style="text-align: center"> <img src="index_files/figure-html/unnamed-chunk-21-1.png" alt="X axis reads pi with values from 0 to 1. Y axis reads f of pi). The curve of the graph has a high peak on the y-axis when pi equals to 0.9. The y-values are almost zero when pi is less than 0.50." /> <p class="caption">X axis reads pi with values from 0 to 1. Y axis reads f of pi). The curve of the graph has a high peak on the y-axis when pi equals to 0.9. The y-values are almost zero when pi is less than 0.50.</p> </div> ] --- ```r plot_beta_binomial(alpha = 3, beta = 8, y = 19, n = 20) ``` <img src="index_files/figure-html/unnamed-chunk-22-1.png" title="X axis reads pi with values from 0 to 1. Y axis reads density. Three curves are shown labeled as prior, (scaled) likelihood, and posterior. The prior curve of the graph has a high peak on the y-axis when pi equals to 0.25 and y values are close to zero when pi is greater than 0.7. The likelihood curve has a high peak on the y-axis when pi equals to 0.95 and is quite peaked with low variance. The posterior sits between the prior and likelihood curves." alt="X axis reads pi with values from 0 to 1. Y axis reads density. Three curves are shown labeled as prior, (scaled) likelihood, and posterior. The prior curve of the graph has a high peak on the y-axis when pi equals to 0.25 and y values are close to zero when pi is greater than 0.7. The likelihood curve has a high peak on the y-axis when pi equals to 0.95 and is quite peaked with low variance. The posterior sits between the prior and likelihood curves." style="display: block; margin: auto;" /> --- <img src="index_files/figure-html/unnamed-chunk-24-1.png" style="display: block; margin: auto;" /> --- class: middle .pull-left[ ### Plotting Functions `plot_beta()` `plot_binomial_likelihood()` `plot_beta_binomial` `plot_gamma()` `plot_poisson_likelihood()` `plot_gamma_poisson()` `plot_normal()` `plot_normal_likelihood()` `plot_normal_normal()` ] .pull-right[ ### Summary Functions `summarize_beta()` `summarize_beta_binomial()` <br> `summarize_gamma()` `summarize_gamma_poisson()` <br> `summarize_normal_normal()` ] --- class: middle ## Model Evaluation Functions | Functions | Response | Model Type | |------------------------------------------------------------------|--------------|------------| | `prediction_summary()` <br> `prediction_summary_cv()` | Quantitative | rstanreg | | `classification_summary()` `classification_summary_cv()` | Binary | rstanreg | | `naive_classification_summary()` `naive_classification_summary_cv()` | Categorical | naiveBayes | --- ## Prediction Summary .pull-left[ ```r prediction_summary(model, data, prob_inner = 0.6, prob_outer = 0.80) ``` ``` mae mae_scaled within_60 within_80 1 4.739019 0.6832428 0.65 0.85 ``` ] -- .pull-right[ ```r prediction_summary_cv(model = model, data = data, * k = 2, prob_inner = 0.6, prob_outer = 0.80) ``` ``` $folds fold mae mae_scaled within_60 within_80 1 1 5.820976 0.7944069 0.5 0.6 2 2 1.976291 0.2052921 0.8 1.0 $cv mae mae_scaled within_60 within_80 1 3.898634 0.4998495 0.65 0.8 ``` ] --- class: middle ## `library(rstan)` .pull-left[ ```r # STEP 1: DEFINE the model stan_bike_model <- " data { int<lower=0> n; vector[n] Y; vector[n] X; } parameters { real beta0; real beta1; real<lower=0> sigma; } model { Y ~ normal(beta0 + beta1 * X, sigma); } " ``` ] .pull-right[ ```r # STEP 2: SIMULATE the posterior stan_bike_sim <- stan(model_code = stan_bike_model, data = list(n = nrow(bikes), Y = bikes$rides, X = bikes$temp_feel), chains = 4, iter = 5000*2, seed = 84735) ``` ] --- class: middle ## `library(rstanarm)` ```r normal_model_sim <- stan_glm(rides ~ temp_feel, data = bikes, family = gaussian, chains = 4, iter = 5000*2, seed = 84735) ``` --- ### `library(bayesplot)` .pull-left[ ```r mcmc_trace(normal_model_sim, size = 0.1) ``` <img src="index_files/figure-html/unnamed-chunk-32-1.png" width="80%" style="display: block; margin: auto;" /> ] .pull-right[ ```r mcmc_dens_overlay(normal_model_sim) ``` <img src="index_files/figure-html/unnamed-chunk-33-1.png" width="80%" style="display: block; margin: auto;" /> ] --- class: middle ## Resources - [Undergraduate Bayesian Education Resources](https://undergrad-bayes.netlify.app/) -- - [Undergraduate Bayesian Education Network](https://undergrad-bayes.netlify.app/network.html) -- - [STATS 115 at UC Irvine](https://www.stats115.com) --- .center[ .middle[ Questions? [bit.ly/dogucu-talks](https://bit.ly/dogucu-talks) ] ] .footnote[<a href="https://www.freepnglogos.com">Images from freepnglogos.com</a>]