Table 2 Experimental procedure.

From: Finding hotspots: development of an adaptive spatial sampling approach

Pseudo code for experiments

1

for rep in \(1\rightarrow 100\):

 

2

   for m in \(\{1, 10, 50\}\):

m = batch size

3

      \({\mathscr {A}}_0 \leftarrow\) random selection: \({\mathscr {A}}_0 \subset {\mathscr {S}}\) with \(\Vert {\mathscr {A}}_0\Vert = 100\)

\({\mathscr {S}} =\) all villages

4

      \({\mathscr {A}}^R_0 = {\mathscr {A}}^A_0 = {\mathscr {A}}_0\)

\(R/A=\)random/adaptive

5

      \(steps = 100 / m\) + 1

total number of iterations

6

      for t in \(1 \rightarrow steps:\)

 

7

         \({y}^{\star}_{i} \sim \text{Binomial}{(100, \theta ({\mathscr{A}^{\star}_{t-1}}))}^{\dagger}\)

\(\star =\{R, A\}\)

8

         \({\mathscr {D}}^\star _{t-1} = \{{\mathscr {A}}^\star _{t-1}, y^\star , \mathbf{x} ({\mathscr {A}}^\star _{t-1}) \}\)

\(\mathbf{x}\)=environmental data

9

         find \(p(\theta > \vartheta | \cup _{k=0}^{t-1} {\mathscr {D}}^\star _k)\)

 

10

         compute validation statistics on \({\mathscr {S}} \setminus \cup _{k=0}^{t-1} {\mathscr {A}}^\star _k\)

 

11

         \({\mathscr {A}}^R_t \leftarrow\) random selection

 

12

         \({\mathscr {A}}^A_t \leftarrow\) acquisition function Eq. (6)

 
  1. We repeated each experiment a hundred times (line 1), for batches of size 1, 10 and 50 (line 2). We started with an initial random sample of 100 locations (line 3) for both random and adaptive methods (line 4). We incorporated subsequent samples until 100 additional sampling locations were added (line 5). For the locations selected to be sampled we simulated the observed positive cases according to a Binomial distribution with prevalence \(\theta\) (line 7) and incorporated the environmental data (line 8). We then used the accumulated data to find the probability of exceeding the threshold \(\vartheta\) (line 9). Finally we defined a new batch of locations according to a random mechanism (line 11) and to the adaptive sampling method proposed (line 12).
  2. \(^{\mathrm{a}}y^R_i = y^A_i\) for step \(t=0\).