Abstract
It is required to estimate exactly the number r of red balls in a population of n balls. The initial distribution of r is uniform on 0, ...,n and further information can be obtained by sampling the balls sequentially without replacement at a cost of (i) 1, (ii) k, (iii) k2 for the kth ball. The problem is normalized by setting the optimal expected payoff for estimating prior to sampling and for estimating after sampling all n balls both equal to zero. Asymptotically as n ↑ ∞ optimal stopping rules are found. Dynamic programs are carried out for n = 15.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 361-368 |
| Number of pages | 8 |
| Journal | Biometrika |
| Volume | 61 |
| Issue number | 2 |
| DOIs | |
| State | Published - Aug 1974 |
| Externally published | Yes |
Keywords
- Bayesian decision theory
- Dynamic programming
- Maximum likelihood estimation
- Optimal stopping
- Sequential sampling
- Urn models
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Agricultural and Biological Sciences (miscellaneous)
- General Agricultural and Biological Sciences
- Statistics, Probability and Uncertainty
- Applied Mathematics