HW 6

Q1.

This question is revisiting Q2 from HW4 but fitting these values as a multivariate response. After enjoying numerous Bridger Bowl powder days during your time at MSU, you have received a job offer in New Mexico. You decision hinges on the quality of snow at your potential new home mountain, Taos.

According to https://www.onthesnow.com/new-mexico/taos-ski-valley/historical-snowfall.html annual snowfall totals can be obtained.

Below are the snowfall totals for Taos and Bridger Bowl for the last nine years.

taos <- c(78,192,169,179,191,204,197,116,195)
bridger <- c(271,209,228,166,316,254,344,319,247)

Specifically you are interested in computing three probabilistic statements.

$Pr[\theta_{bridger} > \theta_{taos}]$ where $\theta_{bridger}$ is the mean annual snow fall at Bridger Bowl and $\theta_{taos}$ is the mean annual snow fall at Taos.
$Pr[\theta_{bridger} > 250]$
$Pr[\theta_{taos} > 200]$

a. (10 pts)

Write out the sampling model and define all parameters. Make sure to specify values in the prior distributions.

b. (30 pts)

Fit a multivariate Gibbs sampler. Include your code in-line here and plot: the posterior distribution for $\theta$ (this will be two dimensional) and the marginal distributions for $\theta_{bridger}$ and $\theta_{taos}$ . Also include the posteriors means for the components in the covariance matrix.

HW 6

Name here

Due Friday October 26, 2018

Q1.

a. (10 pts)

b. (30 pts)

c. (10 pts)