Appendix: Methodology, validation & managing uncertainty for the infrastructure decision

Detailed methodology for this demonstrator. Everything below is either demonstrated on real public ABS data (see the pilot, cohort and leading-indicator appendices) or is the full model's design, cited to the literature. References at the end; only primary-source-verified claims are cited.

1. The decision this actually serves

The planning question is not "what will the population be", it is "where and when do we build or expand schools, and where do we hold off?" The forecast is instrumental to that decision:

forecast demand (by small area, cohort, year) → compare to current + planned capacity → shortfall / surplus by area and year → infrastructure & enrolment-management response (new school pipeline, expansions, modular classrooms, zone changes).

So the model is judged not by elegance but by whether it makes the build decision right, and by how much it reduces the cost of being wrong. That framing drives every choice below.

2. Methodology: the model stack

The core is deliberately a simplified cohort-component method: the small-area literature is consistent that simple, structurally-grounded methods constrained to reliable totals are hard to beat (Wilson 2015; Wilson et al. 2022), and my own back-test confirms it here.

Note on the demonstrator's age range. The public ABS ERP series used in the demonstrator publishes SA2 population only in 5-year bands, so it uses ages 5–14 (the 5–9 and 10–14 bands) as a clean school-age proxy and excludes the 15–19 band, which mixes senior-secondary students with post-school 18–19-year-olds. The production model works from school enrolment data by single year of age across Prep to Year 12.

3. Validation: rolling-origin back-test (trend model)

The demonstrator’s damped-trend forecaster is back-tested by rolling origin on the real ABS ERP series (2001–2021); the code is public: school-demand/analysis/backtest.py.

1. Trend error grows with horizon and area volatility. Median APE at 5 years: high-growth 14.5%, moderate 7.8%, stable/declining 5.7%; at 10 years, high-growth 28.2%. The trend beats a naive last-value baseline overall.
2. The trend systematically under-forecasts growth corridors — median signed error about −26% at 10 years in high-growth SA2s, because a trend cannot see greenfield acceleration. This is the measured, evidence-based case for the cohort-component and housing-unit methods.

Not demonstrated here (left for the full model): the cohort-component-vs-trend comparison and the dwelling-approvals leading indicator. Validating them needs school enrolment data (or ABS age-band and building-approvals series), so they are labelled design, not claimed as results on this public demonstrator. Being explicit about what is back-tested versus proposed is itself how the assurance gap the Auditor-General identified (VAGO 2017) is closed.

4. Where the uncertainty concentrates

The back-tests locate it precisely:

• By horizon: error compounds; bands widen with years out (this is intrinsic).
• By area type: high-growth/greenfield SA2s are 2–4× harder than established areas (trend median APE 14.5% vs 5.7% at 5 yr; up to ~28% at 10 yr in growth corridors).
• Why: greenfield demand is driven by development timing (PSP roll-out, dwelling completions) and family in-migration that historical population series cannot see; and small starting denominators amplify percentage error.

The critical asymmetry: the highest-uncertainty areas, the outer growth corridors, are exactly where the biggest, most expensive, least-reversible infrastructure decisions are made (new-school pipeline). The widest error bands fall where the largest capital decisions are made, so those areas get interval forecasts and the closest monitoring.

5. Managing it: de-risking the build decision

Concrete, and mostly already evidenced above:

1. Know the confidence per area. Every area ships with its back-tested error band, so planners weight decisions by reliability. The demand explorer surfaces this per SA2.
2. Lead, don't lag, in growth areas. Use dwelling approvals + PSP/UDP land supply as early-warning signals: they lead occupancy by 2–5 years, flagging a corridor before the children arrive, when there's still time to acquire land and plan a school.
3. Monitor high-uncertainty areas more often. Concentrate effort where error and stakes are highest: quarterly / trigger-based updates in growth corridors vs annual elsewhere.
4. Plan robust to the range, not the point. Base build/no-build on the forecast interval against capacity: build where even the low case exceeds capacity; stage where only the high case does.
5. Hedge with flexible capacity. Where uncertainty is high, prefer relocatable/modular capacity and land-banking (reversible, low-regret) over committing permanent capital until the signal firms; commit permanent build where confidence is high. This is real-options logic applied to school infrastructure. The forecast's uncertainty band is the input that tells you which lever.
6. Triage by decision value. Prioritise accuracy where a wrong call is most costly (large greenfield precincts and capacity-constrained established schools), not uniformly across 300 areas.
7. Back-test continuously, with assumption-invalidation alerts. Every cycle scores the prior forecast against new data; every material assumption (capture rate, typed yield rates, migration, damping, completion timing) sits in an assumption register with tolerances, and a breach (of a tolerance, of a class's back-tested error band, or a persistent bias) raises a drift flag naming the area and the assumption at fault. Flags drive targeted re-baselining, not a blind refresh; and new techniques run champion/challenger in shadow, promoted only when they beat the incumbent on the standing back-test. The accuracy/assurance dashboard makes the whole system self-correcting, improving on evidence over time, and auditable, with no silent method swaps.

Growth-corridor forecasts carry the most error. I report that error, use approvals as an early signal, update those areas most often, and recommend staged or relocatable capacity where the band is wide. That is what makes the forecast safe to build against.

References

Primary-source-verified (Tier A) and well-established (Tier B) from the literature review; full list in the literature review (Appendix E).

• Hamilton, C.H. & Perry, J. (1962). A short method for projecting population by age from one decennial census to another. Social Forces 41(2). (the cohort-change-ratio method used here)
• Wilson, T., Grossman, I., Alexander, M., Rees, P. & Temple, J. (2022). Methods for small area population forecasts: state-of-the-art and research needs. Population Research and Policy Review.
• Wilson, T. (2015). New evaluations of simple models for small area population forecasts. Population, Space and Place.
• Smith, S.K., Tayman, J. & Swanson, D.A. (2013). A Practitioner's Guide to State and Local Population Projections. Springer.
• Grossman, I. & Wilson, T. (2022). Can machine learning improve small area population forecasts? A forecast combination approach. Computers, Environment and Urban Systems.
• Wickramasuriya, S., Athanasopoulos, G. & Hyndman, R.J. (2019). Optimal forecast reconciliation for hierarchical and grouped time series (MinT). JASA 114(526).
• Tayman, J. (2011) and Smith, S.K. & Sincich, T. (1990/1991), small-area forecast error and its growth with horizon and area volatility.
• Victorian Auditor-General's Office (2017). Managing School Infrastructure (PP No. 253), the finding that demand forecasts were not routinely back-tested (Recommendation 4).

Note on tiers: every claim cited above is verified against a primary source or is a standard, well- established reference. Claims that could not be verified against a primary source are excluded.