class: center, middle, inverse, title-slide .title[ # <p>Teaching Bayesian Statistics at the Undergraduate Level</p> Bayesian Regression and Classification ] .subtitle[ ## ICOTS workshop ] .author[ ### Mine Dogucu ] .date[ ### 2022-09-11 ] --- class: middle ## Models .pull-left[ - Simple Normal Regression - Extending the Normal Regression (multiple predictors, categorical predictors, interaction terms) - Poisson and Negative Binomial regression - Logistic Regression - Naive Bayes classification ] .pull-right[ <img src="img/unit3.png" width="80%" style="display: block; margin: auto;" /> ] --- class: middle ## Modeling Process - Tuning prior models - Simulating the posterior - Posterior prediction - Model evaluation --- <img src="img/bike.jpeg" width="20%" style="display: block; margin: auto;" /> `bikes` ``` ## Rows: 500 ## Columns: 2 ## $ rides <int> 654, 1229, 1454, 1518, 1362, 891, 1280, 1220, 1137, 1368, 13… ## $ temp_feel <dbl> 64.72625, 49.04645, 51.09098, 52.63430, 50.79551, 46.60286, … ``` --- class: middle ## Models **likelihood:** `\(Y_i | \beta_0, \beta_1, \sigma \;\;\;\stackrel{ind}{\sim} N\left(\mu_i, \sigma^2\right)\text{ with } \mu_i = \beta_0 + \beta_1X_i\)` **prior models:** `\(\beta_0\sim N(m_0, s_0^2 )\)` `\(\beta_1\sim N(m_1, s_1^2 )\)` `\(\sigma \sim \text{Exp}(l)\)` --- class: middle ## Goals Statistics goals: simulating the posterior, posterior prediction, model evaluation Pedagogical goals: compute for a single case and then use a built-in function