Skip to main content

Table 5 Variance times cost (i.e., inefficiency, the smaller the better) for one-sample estimator 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

From: Multiple importance sampling revisited: breaking the bounds

 

Example 1

Example 2

Example 3

Example 4

Example EM

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

105.78

17.60

46.82

123.30

14.90

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

40.89

9.37

4.04

300.48

1.32

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

44.43

9.93

3.18

545.53

2.30

\(\alpha _{k} \propto \frac {\sigma _{k,{\text {eq}}}}{\sqrt {c_{k}}}\)

83.82

13.27

33.36

105.80

6.39

\(\alpha _{k} \propto \frac {M_{k,{\text {eq}}}}{\sqrt {c_{k}}}\)

81.66

13.08

30.11

37.57

5.30