1. Methodology
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A more efficient sampling procedure, using loaded probabilities

  1. J Richard Cumpston  Is a corresponding author
  1. JR Cumpston Pty Ltd, Australia
Research article
Volume 5(1) Spring 2012
Cite this article as: J. Richard Cumpston; 2012; A more efficient sampling procedure, using loaded probabilities; International Journal of Microsimulation; 5(1); 21-30. doi: 10.34196/ijm.00065
2 figures and 12 tables

Figures

Figure 1
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Run times with varying simulation cycles.
Figure 2
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Run times with one cycle per year.

Tables

Table 1
Number of draws to give maximum loaded probability of 1.
Number in pool maximum unloaded probability
0.01 0.02 0.05 0.1 0.2 0.5
10 1 1 1 2 3 7
100 2 3 6 11 23 69
1,000 11 21 52 106 224 693
10,000 101 203 513 1,054 2,232 6,932
100,000 1,006 2,021 5,130 10,536 22,315 69,315
Table 2
Simulated event numbers with pools chosen to produce 500 events.
Number low risk persons Low risk rate Number high risk persons High risk rate Expected number of events Mean number from 10,000 trials Standard deviation from 10,000 trials
2,500 0.1 500 0.5 500 499.92 .16
1,250 0.2 500 0.5 500 500.12 .14
833 0.3 500 0.5 500 499.88 .12
625 0.4 500 0.5 500 500.03 .10
500 0.5 500 0.5 500 500.00 .09
Table 3
Table Draws needed to simulate the deaths in a year 175,000 Australians.
Age group Persons in group Average mortality rate Expected deaths Maximum mortality rate Draws
0- 36,441 0.00040 14.5 0.00453 166
15- 23,593 0.00060 14.1 0.00113 27
25- 25,575 0.00087 22.1 0.00138 36
35- 26,810 0.00123 33.0 0.00192 52
45- 24,156 0.00237 57.2 0.00415 101
55- 16,348 0.00642 104.9 0.01315 217
65- 11,852 0.01826 216.4 0.03697 447
75- 7,706 0.05051 389.3 0.10627 866
85- 2,563 0.18238 467.4 0.48496 1701
Total 175,044 0.00754 1,319.0 3,613
Table 4
Areas, person types and age groups used to form pools.
Area code Area name Person type code Person type Age code Age group
1 NSW 1 Partner 1 0–14
2 Victoria 2 Lone parent 2 15–24
3 Queensland 3 Child 3 25–34
4 SA 4 Related person 4 35–44
5 WA 5 Unrelated person 5 45–54
6 Tasmania 6 Lone person 6 55–54
7 NT 7 Group member 7 65–74
8 ACT 8 Non-private resident 8 75–84
9 85-
Table 5
Mean run times in seconds to simulate 175,000 Australians for a year.
Cycles per year All-case trials seconds All-case fitted seconds Loaded trials seconds Loaded fitted seconds Loaded trials as % of all-case
1 1.13 1.58 0.64 0.66 57%
4 4.10 4.14 0.67 0.68 16%
12 11.37 10.98 0.75 0.73 7%
26 23.29 22.94 0.83 0.82 4%
52 44.90 45.15 0.98 0.97 2%
365 2.88 2.88
Table 6
Run times in seconds for projections up to 50 years.
Projection years All-case Yearly Loaded Yearly Loaded Weekly Loaded as% of all case Yearly
1 1.13 0.64 0.98 57%
10 11.59 6.18 9.81 53%
20 24.28 12.82 20.28 53%
30 37.35 19.72 31.2 53%
40 51.93 27.25 42.51 52%
50 66.32 34.16 53.87 52%
Table 7
Event totals from one-year projections, each event simulated separately (50 run averages).
Event Expected Observed all-case yearly Observed loaded yearly Observed loaded weekly
Births 2,170 2,179 2,183 2,208
Deaths 1,372 1,379 1,330 1,370
Emigrants 2,284 2,280 2,251 2,275
Exits 6,254 6,441 6,203 6,592
Moves 12,468 12,411 12,330 12,364
Table 8
Event totals from one-year projections, all events simulated together.
Event Expected Observed all-case yearly Observed loaded yearly Observed loaded weekly
Births 2,170 2,175 2,182 2,232
Deaths 1,372 1,375 1,335 1,375
Emigrants 2,284 2,282 2,263 2,304
Exits 6,254 6,333 6,075 6,611
Moves 12,468 13,418 13,210 12,826
Table 9
Table one-year projections, with events in normal & reverse order (50 run averages).
Event Yearly Weekly
normal order reverse order change in year normal order reverse order change in year
Births 2,182 2,243 61 2,232 2,224 -8
Deaths 1,335 1,331 -4 1,375 1,378 3
Emigrants 2,263 2,308 45 2,304 2,311 7
Exits 6,075 6,540 465 6,611 6,615 4
Moves 13,210 12,323 -887 12,826 12,819 -7
Table 10
50-year projections with yearly cycles (10 run averages).
Event/persons at end All-case yearly mean All-case yearly SD Loaded yearly mean Loaded yearly SD Loaded as % of all-case
Births 102,831 541 101,611 516 98.8%
Deaths 92,205 127 91,924 130 99.7%
Emigrants 123,775 186 123,024 232 99.4%
Exits 355,304 891 347,052 746 97.7%
Moves 797,511 1,716 778,254 937 97.6%
Persons at end 226,755 488 226,566 504 99.9%
Table 11
Standard deviations for one-year projections (based on 50 runs).
Event All-case Yearly All-case Yearly Loaded Yearly Loaded Yearly Loaded weekly Loaded weekly
Expected Observed Expected Observed Expected Observed
Births 43.8 38.6 43.6 38.7 43.5 52.8
Deaths 35.4 32.7 28.0 29.9 31.7 32.2
Emigrants 47.3 38.6 26.2 35.6 36.5 42.8
Exits 73.7 67.6 33.2 39.8 54.7 59.6
Moves 98.3 99.7 10.3 18.9 50.0 55.1
Table 12
Observed coefficients of variation for one-year projections (based on 50 runs).
Event All-case Yearly Loaded yearly Loaded weekly
Births 0.018 0.018 0.024
Deaths 0.024 0.022 0.023
Emigrants 0.017 *0.016 0.019
Exits 0.011 0.007 0.009
Moves 0.007 0.001 0.004

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