Optimally sampling a sequence of observations

Question

Given a multivariate population, I'd like to define a sequence of observations to sample, such that coverage and representativeness is optimal at each step (cumulatively). For example, a sample of five observations would be included in the sample of six, and so on.

I imagine this problem is related to sequential analysis, which is similar in that the marginal observation is chosen to optimize for statistical power. However, it differs in assuming that the marginal observation can be selected after analyzing the cumulative sample; this problem requires selecting the sequence a priori.

Answer 1

One approach that doesn't deal with formal power analysis could

1. Start with the most representative observation, by some measure of central tendency.

2. Select observations which are both similar to unsampled observations, and dissimilar from sampled observations, e.g. weighted 50/50 based on average cosine distance.