Unit 10: Appreciating Bayesian Statistics |
Unit 10: Assignment #1 (due before 11:59 pm Central on THU JUL 20):
- In this Unit, you are going to get an introduction to statistical thinking using Bayesian Statistics.
- To become acquainted with Bayesian Statistics, watch Crash Course’s (2018) video “You Know I’m All About that Bayes.”
- NOTE: The topic of this video, Bayesian Statistics, can be difficult to understand at first.
- Be sure to frequently stop the video, rewind it, and replay any and all sections as often as you need to.
- You’ll be a lot more successful gaining an understanding of Bayesian Statistics from watching this video if you treat it more like a textbook than a typical YouTube video.
- After watching this video, make sure you know the answers to these eight questions:
- What is Bayes’ Theorem (also called Bayes’ Rule)?
- How does Bayes’ Theorem allow us to update our beliefs based on new information?
- How can Bayesian statistics be used to test hypotheses?
- What is a Bayes Factor?
- What is a Prior Probability (in Bayesian Statistics)?
- What is a Posterior Probability (in Bayesian Statistics)?
- What role does evidence play in Bayesian Statistics?
- What is the core idea of Bayesian Hypothesis Testing?
- For each of the eight questions listed in c. above, write four multiple-choice answers
**.**
- For each question, one of the four multiple-choice answers should be the correct answer to the question; the other three multiple-choice answers should be incorrect answers to the question.
- Like all good multiple-choice questions, your wrong multiple-choice answers shouldn’t be too obviously wrong.
- Go to Unit 10: Assignment #1 Discussion Board and make a new Discussion Board post in which you list the eight questions (from c. above) and the four multiple-choice answers you created for each question.
**Use bolding to indicate the correct multiple-choice answer for each question**.
- To get more familiar with using Bayesian statistics:
- First, read Wagenmakers’ (2020) children’s book, “Bayesian Thinking.”
- Although written for children, Wagenmakers’ book illustrates Aunt Agatha’s use of
- a prior probability (hypothesis): At the outset, Aunt Agatha didn’t know whether Kate or Miruna knew the most about dinosaurs, so she initially was going to divide the cookies evenly;
- posterior (updated) probabilities (hypotheses): After the Triceratops question, Aunt Agatha updated her hypothesis to be that Kate knew more than Miruna about dinosaurs, but after the Stegosaurus question, Aunt Agatha updated her hypothesis to be that Miruna knew more than Kate about dinosaurs; and
- the role of evidence in Aunt Agatha updating her likelihood probability.
- Although written for children, Wagenmakers’ book illustrates Aunt Agatha’s use of
- Second, read Gleeson’s (2021) article, “Bayes’ Rule – Explained For Beginners.”
- While reading Gleeson’s article, make sure you understand the following:
- Prior Probability
- Posterior Probability
- Likelihood Probability
- Marginal Probability
- Conditional Probability (which we covered in Unit 6)
- Gleeson’s “Worked Example” of Bayes’ Rule
- While reading Gleeson’s article, make sure you understand the following:
- Third, look through Huys and Mirza’s four slides from their (2016) presentation “Bayes for Beginners,” which contains another labeled equation for your reference.
- Third, create your own “Worked Example” of Bayes’ Rule that is similar to Gleeson’s (2021) “Worked Example.”
- You can use any topic you want to for your “Worked Example.”
- However, make sure that your “Worked Example,” similar to Gleeson’s (2021) “Worked Example,” has a Prior Probability, Posterior Probability, Likelihood Probability, and Marginal Probability.
- Like Gleeson’s “Worked Example,” your “Worked Example” should have both a
**narrative description**of the situation AND**a mathematical equation**.
- First, read Wagenmakers’ (2020) children’s book, “Bayesian Thinking.”
- Go to Unit 10: Assignment #2 Discussion Board and make a new Discussion Board post in which you provide the “Worked Example” of Bayes’ Rule that you created.
- To become even more familiar with Bayesian statistics, do the following:
- Read Kurt’s (2019) Chapter 1.
- NOTE: This is a copyrighted and password-protected PDF; to read the PDF, you’ll need to type in a password.
- The password is the email subject heading you’re supposed to use in this course when you email a question.
- Capitalization, punctuation, and spacing matter for this password.
- If you’re initially unable to open the PDF, and you’re sure you’re inputting the correct password:
- Try a different browser. Some browsers are set to a default level of security that interferes with opening password-protected files. Using a different browser (which is a good go-to solution for a lot of Internet-related problems) should help.
- Or save the PDF onto your own computer, and open the PDF there (using Adobe Reader, Preview, or another PDF reader), rather than trying to open the PDF in your browser.
- This chapter is considerably more complex (and longer!) than the other reading assignments in this course; therefore, while you’re reading this chapter do the following:
- Take notes on every new concept.
- Self-test yourself; in fact, read ahead to the activities at the end of the chapter and make sure, as you’re reading through the chapter, you’ll be able to complete the activities.
- Re-read anything you’re not perfectly confident you understand.
- Read and re-read in several short periods, rather than in one sitting.
- Consider setting a Pomodoro or other timer so that you read and study the chapter for 10 to 15 minutes; then take a 5- to 10-minute break.
- Re-set your Pomodoro timer and read and study for another 10 to 15 minutes; then take a 5- to 10-minute break.
- The above suggestions are useful for reading any textbook chapter in any course!
- While you’re reading this chapter, make sure you understand the following:
- Bayesian statistics comprise the formal process we use to update our assumptions about the world once we’ve observed data.
- Data inform assumptions; assumptions should not inform data.
- In formulas expressing Bayesian statistics, we use a comma to separate events when we’re looking at the combined probability of multiple events.
- In formulas expression Bayesian statistics, we enter prior assumptions after our data, separated with a |
- Read Kurt’s (2019) Chapter 1.
- Go to the Unit 10: Assignment #3 Discussion Board and make a new Discussion Board post in which you provide the answers to the three activities at the end of the chapter.
- To become even more familiar with Bayesian statistics, watch Crash Course’s (2018) video “Bayes in Science and Everyday Life.”
- Again, be sure to frequently stop the video, rewind it, and replay any and all sections as often as you need to.
- Again, you’ll be a lot more successful gaining an understanding of Bayesian Statistics from watching this video if you treat it more like a textbook than a typical YouTube video.
- While watching this video, be sure to recognize six examples of using Bayes Statistics in science as well as everyday life:
- getting more clicks through an advertising email;
- finding out if people with Dissociative Identity Disorder have different memories between their personalities;
- predicting which future items people will buy based on the previous items those people bought;
- translating texts into different languages;
- using genetic profiles to predict sensitivity to allergy medication; and
- programming ‘smart assistants’ like Siri to understand spoken language.
- Think of
**one more use**of Bayes Statistics in**either**everyday life**or**science. - Go to the Unit 10: Assignment #4 Discussion Board and make a new Discussion Board post of
**at least 200 words**in which you describe the example you thought of for using Bayes Statistics in either science or everyday life.
- Meet online with your NEW Chat Group (which you formed during Unit 8) for a one-hour text-based Group Chat at a time/date that your Chat Group previously arranged.
**BEFORE YOU MEET WITH GROUP CHAT**do the following:- First, read
**Part ONE**of Langewiesche’s (2019) article, “What Really Happened to Malaysia’s Missing Airplane?”- NOTE: This article is about the disappearance of Malaysia Airlines Flight 370 in March 2014. If that topic is uncomfortable for you, please contact Dr. Andrews for an alternative assignment.
- Second, after reading Part ONE (and only Part ONE) of this article, generate initial hypotheses about what caused the plane to disappear (e.g., the plane was high-jacked, the plane crashed into the ocean, or the plane remained intact but the radar malfunctioned).
- These hypotheses will be your prior hypotheses (i.e., prior beliefs).
- Assign a probability to each of your prior hypotheses.
- During the Group Chat, when you read more of the article, you will adjust your prior hypotheses, but
**DO NOT**read farther than Part ONE until your Chat Group begins their one-hour Group Chat.
- First, read
**DURING YOUR ONE-HOUR GROUP CHAT**do the following:- First, begin your chat with each Chat Group member indicating ONE of the nine “How Are You Feeling at the START of Today’s Group Chat?” images. More than one Chat Group member can indicate the same image if that’s how they are feeling, and please refer to each image by its number.
- Second, all Chat Group members should read (during the Group Chat)
**Part TWO**of Langewiesche’s (2019) article, “What Really Happened to Malaysia’s Missing Airplane?”- After all Chat Group members have finished reading
**Part TWO**, discuss — as a group — how you should update your prior hypotheses to create your current posterior hypotheses. - Assign probabilities to your current posterior hypotheses.
- After all Chat Group members have finished reading
- Next, all Chat Group members should read (during the Group Chat)
**Part THREE**of Langewiesche’s (2019) article, “What Really Happened to Malaysia’s Missing Airplane?”- After all Chat Group members have finished reading
**Part THREE**, discuss — as a group — how you should update your prior hypotheses to create your current posterior hypotheses. - Assign probabilities to your updated posterior hypotheses.
- After all Chat Group members have finished reading
- Finally, all Chat Group members should read (during the Group Chat)
**Part FOUR**of Langewiesche’s (2019) article, “What Really Happened to Malaysia’s Missing Airplane?”- After all Chat Group members have finished reading
**Part FOUR**, discuss — as a group — how you should update your prior hypotheses to create your final posterior hypotheses. - Assign probabilities to your final posterior hypotheses.
- After all Chat Group members have finished reading
**AT THE END OF YOUR ONE-HOUR GROUP CHAT**do the following:
- Each Chat Group member needs to indicate ONE of the nine “How Are You Feeling at the END of Today’s Group Chat?” images. More than one Chat Group member can indicate the same image if that’s how they are feeling, and please refer to each image by its number.
**NOTE**: The “How Are You Feeling at the**END**of Today’s Group Chat” grid of images differs from the “How Are You Feeling at the**START**of Today’s Group Chat” grid of images.
- Nominate one member of your Chat Group (who participated in the Chat) to make a post on the Unit 10: Assignment #5 Discussion Board that summarizes your Group Chat in at least 200 words. This Chat Group member should not post their 200-word summary of your Group Chat until they have completed their Course Journal for the current Unit.
- At the end of the 200-word summary, this member needs to write this sentence filling the blanks: “I have completed my Course Journal for the current Unit. It contains ___ words and the two things I learned during this Unit about which I journaled about are ___ and ___.”
- Nominate a second member of your Chat Group (who participated in the Group Chat using the browser Chrome on their laptop, rather than on their mobile device) to save the Chat transcript, as described in the Course How To (under the topic, “How To Save and Attach a Chat Transcript”).
- This Chat Group member needs to make a post on the Unit 10: Assignment #5 Discussion Board and attach the Chat transcript, saved as a PDF, to that Discussion Board post. This Chat Group member should not post the transcript of your Group Chat until they have completed their Course Journal for the current Unit.
- In their Discussion Board post, this member needs to write this sentence filling the blanks: “I have completed my Course Journal for the current Unit. It contains ___ words and the two things I learned during this Unit about which I journaled about are ___ and ___.”
- Remember to attach the Chat transcript by clicking on the word “Attach.” (Do not click on the sidebar menu “Files.”)
- This Chat Group member needs to make a post on the Unit 10: Assignment #5 Discussion Board and attach the Chat transcript, saved as a PDF, to that Discussion Board post. This Chat Group member should not post the transcript of your Group Chat until they have completed their Course Journal for the current Unit.
- Nominate a third member of your Chat Group (who also participated in the Chat) to make another post on the Unit 10: Assignment #5 Discussion Board that states the name of your Chat Group, the names of the Chat Group members who participated in the Chat, the date of your Chat, and the start and stop time of your Group Chat. This Chat Group member should not post the names, date, and times of your Group Chat until they have completed their Course Journal for the current Unit.
- In their Discussion Board post, this member needs to write this sentence filling the blanks: “I have completed my Course Journal for the current Unit. It contains ___ words and the two things I learned during this Unit about which I journaled about are ___ and ___.”
- This Chat Group member also needs to include in their post each group member’s initial prior hypothesis and the group’s final posterior hypothesis.
- If only two students participated in the Group Chat, then one of those two students needs to do two of the above three tasks.
- Before ending the Group Chat, arrange the date and time for the Group Chat you will need to hold during the next Unit (Unit 11: Assignment #5).
- Each Chat Group member needs to indicate ONE of the nine “How Are You Feeling at the END of Today’s Group Chat?” images. More than one Chat Group member can indicate the same image if that’s how they are feeling, and please refer to each image by its number.
Congratulations, you have finished Unit 10! Onward to Unit 11! |