Hello!

Here are some materials for a guest lecture given on Bayesian Demography as part of the ‘Advanced Demographic Methods’ (DEMG7310 / POP514) course.

Packages to install

If you would like to follow along with the coded examples, as well as having R and RStudio installed, you will need to install the following packages:

• tidyverse
• rstan
• rstanarm
• tidybayes
• janitor
• rcbayes

The rstan package is probably the most important but could be annoying to install. If you have issues, see detailed instructions here: https://github.com/stan-dev/rstan/wiki/RStan-Getting-Started

Lecture slides

pdf version is here.

Lab materials

There are three labs written in Quarto files. (in the labs folder). The data and models required to compile the Quarto documents are also in their respective folders. A pdf version of each lab is listed below.

• Gompertz
• SVD
• Rogers Castro

Optional exercise

Here is an optional exercise based on the Gompertz lab.

1. Download or read in the Deaths and Population data for Quebec from the Canadian Human Mortality Database
2. Plot mortality rates on the log scale for ages 40+ for females in years 1940, 1980, and 2020.
3. Fit a Gompertz model in Stan separately for each year specified above for females aged 40-105. Make some plots that show the estimates for log(alpha) and beta for each of the years (geom_point with geom_errorbar would be suitable here)
4. Now fit a dynamic Gompertz model for all years between 1940 and 2020 with a random walk on both log(alpha) and beta. Compare the resulting estimates to those in Step 3. How similar or different are they? What are the advantages and disadvantages of each approach?
5. Rather than a random walk model on log(alpha) and beta as in 4, imagine you would like to model these parameters with a quadratic function of time. How would you implement this in Stan?