class: center, middle, inverse, title-slide # Introduction to Bayesian Analysis ### Dr. Dogucu --- layout: true <div class="my-header"></div> <div class="my-footer"> From Bayes Rules! book Copyright &copy; Drs. Alicia Johnson, Miles Ott & Mine Dogucu. <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a></div> --- # Key Point in Bayesian Statistics It is OK - to have prior ideas (e.g. expert knowledge) - use these ideas - weight them against the observed data. --- # Bayesian vs. Frequentist Consider two claims. (1) Zuofu claims that he can predict the outcome of a coin flip. To test his claim, you flip a fair coin 10 times and he correctly predicts all 10! (2) Kavya claims that she can distinguish Dunkin' coffee from Starbucks coffee. To test her claim, you give her 10 coffee samples and she correctly identifies the origin of each! In light of these experiments, what do you conclude? a. You're more confident in Kavya's claim than Zuofu's claim. b. The evidence supporting Zuofu's claim is just as strong as the evidence supporting Kavya's claim. --- # Bayesian vs. Frequentist Your doctor called you to tell you that you have been tested positive for a rare disease. The doctor gives you the opportunity to ask one question. Which of the following would you ask? a. What is the probability that I actually have the disease given that I have tested positive? b. If I do not have the disease, what is the probability that I would have gotten this positive test result? --- # Notes on Bayesian History - Frequentist statistics is more popular and Bayesian statistics is starting to get popular. - Named after Thomas Bayes (1701-1761). - Computing, computing, computing. - It is harder to adopt to newer methods. Thus change is happening slowly. - We can embrace subjectivity. --- # Bayesian vs. Frequentist .pull-left[ __Frequentist__ Probability is based on long-term frequencies. When answering a question, we assume that the null hypothesis is true and then calculate the probability of observing the data if the null were true. ] .pull-right[ __Bayesian__ Probability is a balance of relative plausibility of an event and degree of prior ideas. When an answering a question we calculate the probability that the null hypothesis is true based on the given data. ] --- # Optional Watch [How Data Nerds Found A 131-Year-Old Sunken Treasure](https://fivethirtyeight.com/features/how-data-nerds-found-a-131-year-old-sunken-treasure/) Spoiler alert: They used Bayesian Statistics!