Maps of parasite prevalences and other aspects of infectious diseases that vary in space are widely used in parasitology. However, spatial parasitological datasets rarely, if ever, have sufficient coverage to allow exact determination of such maps. Bayesian geostatistics (BG) is a method for finding a large sample of maps that can explain a dataset, in which maps that do a better job of explaining the data are more likely to be represented. This sample represents the knowledge that the analyst has gained from the data about the unknown true map. BG provides a conceptually simple way to convert these samples to predictions of features of the unknown map, for example regional averages. These predictions account for each map in the sample, yielding an appropriate level of predictive precision.
The need for Bayesian geostatisticsA recently described, large database of Plasmodium falciparum endemicity surveys in Africa and Yemen [1,2] is shown in Figure 1 in two and three dimensions. The data are highly clustered and coverage is sparse in Central Africa. The short-range variation in the data is striking; for example, in the small cluster to the east of Lake Victoria, where observed prevalences range widely from zero to near 80%. Efforts to account for this variability by means of environmental factors [3][4][5], time [2], and age [6] are ongoing, but much of it remains unexplained, possibly because local variation in environment and human activities are not captured by the environmental data available at continental scales.These observations call into question the usefulness of producing a single map of P. falciparum endemicity in Africa and elsewhere. A map provides a single estimate for each location in the mapped region, and it is clearly impossible to make accurate and precise estimates of parasite rates in Central Africa based on the sparse data coverage there. Even if data coverage were uniformly dense, the unexplained short-range variability evident in datarich East Africa indicates that no single value would capture the wide range of endemicities that might be encountered at an unsampled location. The malaria epidemiology community faces the problem of converting this patchy dataset, with substantial unexplained variation, into advice for a range of users.Bayesian geostatistics (BG), which is becoming the standard mapping technique in certain branches of parasitology [7], is well suited to generating advice under uncertainty because it attempts to find a large sample of maps that are consistent with the dataset rather than a single map. This sample is encapsulated in the posterior distribution. This opinion is a guide
Posterior distributionsA posterior distribution, often called a posterior, is a probability distribution that has been informed by data according to the rules of Bayesian inference [8]. Figure 2 shows a probability distribution for a random number labeled X. In the Bayesian interpretation of probability, 'random' just means 'unknown;' random numbers such as X are understood to have unkn...