Project 2: Fall 2024

Groups:

• Adelies: Vera, Sarlina, Lionel, RK, Killian, Johnny

• Chinstraps: Heather, Maria, Hailee, Carolyn, Liz, Sara

• Gentoos: Chris, Catherine, Andee, Curtis, Hooman, Jacob.

Set Up:

• Let \(\mu\) denote the typical flipper length (in mm) among the penguin species your group was assigned. To learn about \(\mu\), we’ll utilize flipper measurements \((Y_1, Y_2, ..., Y_n)\) on a sample of penguins.

• The penguins_bayes data in the bayesrules package contains data on the flipper lengths for a sample of three different penguin species. For the species you were assigned, you will disseminate an analysis on penguin flipper length.

Deliverable 1: a presentation on Monday, November 25.

• Slide 1: Introduce your penguin species and the measure(s) we are interested in estimating.

• Slide 2: Explain which Bayesian model is appropriate for this analysis: Beta-Binomial, Gamma-Poisson, or Normal-Normal.

• Slide 3: Do some basic research to determine what the average flipper length for your species is.

  • Note: you should not calculate anything here. You should obtain plausible values.

• Slide 4: Specify (and justify) an appropriate prior model for \(\mu\).

• Slide 5: Describe the sample data.

  1. How many data points are there?
  2. What is the sample mean and standard deviation of flipper length?
  3. Construct a histogram of this species’ flipper length.

• Slide 6: Specify the posterior model for \(\mu\).

• Slide 7: Calculate and interpret a middle 95% posterior credible interval for \(\mu\).

• Slide 8: State the corresponding hypotheses using \(H_0\), \(H_1\), and \(\mu\) . We suspect that there are more and more extra large penguins, so we hypothesize that the average flipper length is somewhere between (note: this is a two-sided hypothesis test!):

  • Adelies: 210 and 220 mm
  • Chinstraps: 215 and 225 mm
  • Gentoos: 240 and 250 mm

• Slide 9: Use the credible interval previously constructed to draw a conclusion about the hypotheses on the previous slide.

• Slide 10: Calculate and interpret the posterior probability that your hypothesis is true. Do you still agree with the conclusion you drew in the previous slide?

• Slide 11: Find the Bayes’ Factor for these hypotheses. Explain how this supports your decision in the previous slides.

• Slide 12: Summarize your findings: explain your conclusion about \(\mu\) based on the evidence gathered / shown in previous slides.

Deliverable 2: assessment of presentations.

• Copy this Google Doc to your account and fill out as you watch presentations.