mrc-ide/Africa_MMS_design

Holds analysis associated with a paper attempting to put bounds on how much malaria molecular surveillance is needed in Africa # DR Hotspot Analysis Spatiotemporal Bayesian analysis of K13 antimalarial-resistance markers in aast Africa, by exact Gaussian-process MCMC. ## Overview Three K13 mutations associated with artemisinin partial resistance are modelled **jointly** across space and time: | Marker | Region | Bounding box (lon / lat) | |--------|--------|--------------------------| | **622I** | Ethiopia / Horn of Africa | 30–45 / 4–18 | | **675V** | DRC / Uganda | 28–38 / −1–6 | | **561H** | Tanzania / DRC border | 27–33 / −5–1 | Site-level prevalence data come from the STAVE dataset (pinned to commit `2d85d02`), filtered to 2010 onward; one row is one prevalence estimate per site-visit. The analysis fits a family of separable space-time Gaussian-process (GP) models to binomial prevalence under a logit link, using **exact full-N MCMC** (Stan / NUTS) — no INLA/SPDE or other approximation. All three markers are fit in a **single joint model** that shares the spatial length scale across markers through a hierarchical (random-effect) prior, while keeping every other parameter marker-specific. Model comparison (WAIC + posterior-predictive RMSE) selects the best covariance structure, which is then used to produce posterior maps of mean prevalence and uncertainty on a dense spatiotemporal prediction grid. **Selected model: `const_AR1_exp_nug`** — an exponential spatial kernel with a separable continuous-time AR1 temporal term, an observation nugget, and an intercept-only mean. It wins outright on joint WAIC (top-4 are all AR1·exp, ΔWAIC ≤ 6.6, then a ~15-point gap to the next cluster). ## The joint model A single Stan fit (`R/stan_models/gp.stan`) stacks all three markers. Because the markers occupy disjoint regions, the joint covariance is **block-diagonal**, so the per-gradient cost is Σ O(N_m³), not O((ΣN)³). Sharing is at the hyperparameter level only: - `log l_space[m] ~ Normal(mu_ls, tau_ls)` — hierarchical spatial length scale (non-centred), pooled across markers; - everything …