Table 3 Variances for one-sample balance heuristic for the four examples in Appendix C and the environment map example (× 10⁻³) for balance heuristic using equal count of samples, for the count inversely proportional to the variances of independent estimators [9] and [10], and for the three new estimators defined in this paper

Ex. 1

Ex. 2

Ex. 3

Ex. 4

Ex. EM

\(\alpha _{k} \propto \frac {1}{n}\)

30.16

5.02

13.35

35.16

5.14

\(\alpha _{k} \propto \frac {1}{v_{k}}\) [9, 10]

24.22

4.60

2.05

332.97

1.50

\(\alpha _{k} \propto \frac {1}{m^{2}_{k}}\)

27.04

4.85

0.39

863.50

3.46

α _k ∝σ_k,eq

31.03

5.10

11.67

57.38

4.84

α _k ∝M_k,eq

29.07

4.92

8.72

22.59

4.28