The Gambia 2074

The Gambia has no complete civil registration. Deaths go largely unrecorded, so there is no national time series of age-specific death rates, and the country is absent from the Human Mortality Database, the standard input for mortality forecasting. Every long-range public decision still runs on population projections: how many classrooms to build, how large the future labour force and pension bill will be, how many clinics to staff. The only figures available are the UN's. Those were finalised before The Gambia's first-ever digital census in 2024. I wanted to build an independent projection, based on the 2024 census, with uncertainty quantified, that a Gambian could check and a planner could use.

• Lee & Carter's 1992 paper is the basis for the model. The single-index log-bilinear structure (log m(x,t) = a_x + b_x k_t) is the backbone of every mortality forecast the UN publishes. The classical SVD version was the first implementation, as a transparent baseline.
• Brouhns, Denuit & Vermunt (2002) is the Poisson log-bilinear approach. The standard SVD assumes homoskedastic Gaussian errors on log-rates, which is wrong where death counts are small and noisy. Exactly The Gambia's case. Poisson-on-deaths is the principled fix and the basis for the Bayesian version.
• Li & Lee (2005) is the coherent forecasting method. A single small-population forecast can drift to implausible long-run mortality. The coherent extension forecasts a country jointly with a reference group so it cannot diverge, and it is why the model pools The Gambia with seven West-African neighbours.
• Raftery et al. (2012, PNAS) is the Bayesian hierarchical method the UN adopted for WPP in 2015. Understanding it was necessary before benchmarking against WPP rather than just citing it.
• Preston, Heuveline & Guillot's 'Demography' Ch. 6 is the reference for the cohort-component method: survivorship ratios from life tables, Leslie-matrix accounting, the open-age interval.
• The Human Mortality Database does not list The Gambia. The thing that made the project feasible is the Farafenni Health & Demographic Surveillance System, running since 1981, and Basse since 2007. Rare multi-decade empirical mortality data for a sub-Saharan country.

• No civil registration, no national age-specific death-rate series, The Gambia is absent from the HMD. Any model runs on reconstructed or surveillance data, and pretending otherwise would be indefensible to an examiner.
• The UN WPP data portal's /data API is token-gated (returns 401 without a generated bearer token), so the obvious programmatic route was closed.
• Mid-project the machine's C: drive hit ~50 MB free. The PyMC conda environment, which pulls a multi-GB compiler toolchain, could not install.
• PyMC on Windows had no C++ compiler available, so PyTensor fell back to its slow no-compiler mode.
• Examiner-grade accuracy: every figure had to regenerate from public data, and I refused to invent any number I couldn't source (I left the exact census total flagged for verification rather than guess).

1. Decision 01

   Make the data-scarcity limitation the research question, not a footnote.

   The obvious version of this project is to fit Lee-Carter to the available series and publish a point estimate. That leaves the central problem, no national death registration, unaddressed. So I reframed: how does one build a credible, uncertainty-honest projection for a country with no death registration, and how much do the answers depend on the method and the data vintage?

2. Decision 02

   Pin the data to the UN team's open R package, not the token-gated API.

   When the /data API returned 401, I found that the UN Population Division's own `PPgp/wpp2024` R package publishes the WPP series as plain text in its data-raw directory. I pinned to a specific commit SHA, streamed each (sometimes 50 MB) file, kept only The Gambia's rows, and wrote a checksummed manifest. No token, exact commit version, and it sidestepped the disk limit because the full multi-country files never touch disk.

3. Decision 03

   Bayesian Poisson Lee-Carter with a_x fixed and b ~ Dirichlet(1).

   Estimating a_x, b_x and k_t jointly creates the classic Lee-Carter identifiability ridge, and NUTS would not mix (r-hat ~1.02). Fixing a_x at the empirical mean log-rate (which is literally how Lee & Carter define it) and constraining b to the simplex via a Dirichlet removed the ridge and let the chains converge, while still propagating full parameter and forecast uncertainty into life expectancy.

4. Decision 04

   Validate the projection engine against WPP before trusting it with my own inputs.

   A cohort-component engine has a hundred places to get an index or a survivorship ratio subtly wrong. So I fed it WPP's own mortality, fertility, sex-ratio and migration and checked that it reproduced WPP's published projection. It matched to within 0.3 to 0.9% through 2074. Only then did I swap in the census base and my own mortality.

5. Decision 05

   Re-base the whole projection on the 2024 census, and vectorise it over 1,000 simulations.

   WPP's 2023 population is ~13% above the new census, so starting from WPP would bake in the overcount. I reconciled the base to the census total and its broad age structure, then ran the cohort-component model over 1,000 simulated mortality and fertility futures, carrying the population as an (age × simulation) matrix, which vectorises the run and produces credible intervals rather than a single line.

• The UN WPP /data API returned 401 across every variant I tried. Instead of chasing a token, I reverse-engineered the download site, found it builds file URLs from a runtime manifest, and then discovered the cleaner source entirely: the UN team's `PPgp/wpp2024` package on GitHub. Pinned a commit, streamed and filtered to Gambia. The blocker turned into a more citable, more reproducible pipeline.
• The PyMC conda environment failed mid-install with 'No space left on device', the disk was at 50 MB. I cleared regenerable caches, confirmed system Python already had numpy/scipy/pandas, and installed PyMC lean via pip into system Python rather than the multi-GB conda toolchain. The Bayesian model that 'needed' conda ran fine on a 200-line pip install.
• The first Bayesian fit would not converge. The 101-dimensional Dirichlet plus a free a_x left a ridge in the posterior. Fixing a_x at the empirical mean (the classical definition) dropped max r-hat from ~1.02 to 1.010 and lifted the effective sample size into the thousands for the parameters that matter.
• Halfway through I noticed WPP's 2023 population (2,728,905) sits about 13% above the 2024 census (around 2.42M), and runs above every historical Gambian census too. WPP was finalised before the census came out, so I rebuilt the projection on the census base.

• This was my first time fitting Lee-Carter in a fully Bayesian framework. I learned why the identifiability constraints (sum of b = 1, sum of k = 0) exist the hard way, by watching chains refuse to mix until I imposed them properly.
• PyMC sampled without a C compiler, so a single 4-chain run took ~8 minutes. I learned to validate the model on a short run (and on synthetic data with known parameters) before committing to longer ones, and to background the long runs.
• The open-ended 100+ age group in the Leslie matrix is genuinely fiddly. Rather than fake precision I used a one-year survival approximation for the open group and confirmed it doesn't move the national totals or dependency ratios, because almost no one is over 100.

• Eleven reproducible modules, from data fetch and life tables through the classical, Bayesian and coherent mortality models to the projection engine and validation
• Life table reproduces WPP's published e0(2023) of 65.86 exactly
• Lee-Carter backtest (fit up to 2010, predict 2011 to 2023): 0.65-year mean error, with the truth inside the 95% range every year
• The three mortality methods agree on life expectancy in 2074 to within about 0.8 years.
• Cohort-component engine validated to within 1% of WPP's published projection
• Population reaches 4.66M by 2074 (range 4.35 to 4.98M), from a census base rather than the UN's pre-census estimate
• The demographic dividend quantified: the dependency ratio falls from 77 to 49 while old-age dependency triples
• Full research report plus a plain-language policy brief written for Gambian media and planners

I haven't yet digitised the Farafenni and Basse HDSS published life tables or run a GBD cross-check. Both would turn the validation chapter from 'validated against the UN's reconstruction' into 'validated against independent empirical Gambian data'. I flagged them as remaining data tasks rather than inventing numbers. I'd also fit the Bayesian model sex-specifically for the projection and add the UN's own bayesPop as a fourth benchmark.