ANLY505 - Intro to Stan

knitr::opts_chunk$set(echo = TRUE)
suppressPackageStartupMessages(library(rstan))
suppressPackageStartupMessages(library(gdata))
suppressPackageStartupMessages(library(bayesplot))
suppressPackageStartupMessages(library(parallel))

Intro to STAN Homework

After our Intro to Stan lecture I think it would be valuable to have you go through a similar exercise. Let’s test a second research question.

Research question: Is sea ice extent declining in the Southern Hemisphere over time? Is the same pattern happening in the Antarctic as in the Arctic? Fit a Stan model to find out!

Make sure you follow the steps we used in class.

1. Load and Inspect Data

#place the code here

2. Plot the data

#plot data

3. Run a general linear model using lm()

#write the code

4. Index the data, re-run the lm(), extract summary statistics and turn the indexed data into a dataframe to pass into Stan

#write the code here

5. Write the Stan model

#write the code

 write("// Stan model for simple linear regression

data {
 int < lower = 1 > N; // Sample size
 vector[N] x; // Predictor
 vector[N] y; // Outcome
}

parameters {
 real alpha; // Intercept
 real beta; // Slope (regression coefficients)
 real < lower = 0 > sigma; // Error SD
}

model {
 y ~ normal(alpha + x * beta , sigma);
}

generated quantities {
} // The posterior predictive distribution",

"stan_model1.stan")


stan_model1 <- "stan_model1.stan"

6. Check to see how many cores your computer has and enable parallel computing

detectCores(all.tests = FALSE, logical = TRUE)

options(mc.cores = parallel::detectCores())

7. Run the Stan model and inspect the results

#code here

8. Extract and inspect the posterior estimates into a list so we can plot them

#code here

9. Compare your results to our results to “lm”

#code here

10. Plot multiple estimates from the posterior

#code here

11. Change the priors and see how that affects your results

#code here

12. What happened when you changed the priors? Does the model fit better or not?

13. Convergence diagnostics - create traceplots that show all 4 chains

#code here

14. Plot parameter summaries for:

\(\alpha\), \(\beta\), \(\sigma\)