Please use D2L to turn in both the PDF output and your R Markdown file.

Q1.

Read Andrew Gelman and Cosma Shalizi’s Philosophy and the Practice of Bayesian Statistics, a link is available on the course webpage. The paper is a little long, so the following questions are designed to focus your reading.

a. (8 pts - 1/2 page or so)

Summarize the key points in the paper. Hint: see section 7.

b. (4 pts - 1/4 page or so)

Summarize Section 4.1

c. (4 pts - 1/4 page or so)

Describe the data analysis cycle, both from a frequentist and Bayesian perspective.

d. (4 pts - 1/4 page or so)

How do the hypothetico-deductive and inductive philosophical view points on science differ?

Q2. (8 pts)

Describe the differences between Bayesian and classical inference. Include a discussion on confidence and credible intervals. Do you currently consider yourself a Bayesian or classical statistician (no wrong answers here)?

Q3.

Assume you are hired by Bridger Bowl to compute the probability than an MSU student either skis (or snowboards).

a. (4 pts)

If binary data is collected from 300 students, what is the sampling model for this research question? Please name the distribution and write out the corresponding sampling distribution.

b. (4 pts)

Use a prior distribution from the \(Beta\) distribution and create a plot/histogram from this distribution. Hint: dbeta() will be useful. Why did you choose the \(\alpha\) and \(\beta\) values for this prior distribution.

c. (4 pts)

Assume 234 of the sampled MSU students claim to either ski or snowboard. Compute the posterior distribution, \(p(\theta|Y)\) where \(\theta\) is the probability of MSU student skiing and \(Y\) is the observed responses.

d. (4 pts)

Plot the posterior distribution computed in part (c) and compute a 95% credible interval for \(\theta\).

e. (4 pts - 1/4 page or so)

Summarize the results for the director of Bridger Bowl, who you can assume has not taken a statistics course recently.