---
title: "HW 1"
author: "Name here"
date: "Due Friday September 7, 2018"
output: html_document
---

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.