Computer Intensive Techniques

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Computer Intensive Techniques (Bootstrapping)
Instructor Ron S. Kenett Email
ron_at_kpa.co.il Course Website www.kpa.co.il/biosta
t Course textbook MODERN INDUSTRIAL
STATISTICS, Kenett and Zacks, Duxbury Press, 1998
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Course Syllabus

• Understanding Variability
• Variability in Several Dimensions
• Basic Models of Probability
• Sampling for Estimation of Population Quantities
• Parametric Statistical Inference
• Computer Intensive Techniques
• Multiple Linear Regression
• Statistical Process Control
• Design of Experiments

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Bootstrapping

• A computer intensive method, introduced in 1979
  by Brad Efron from Stanford University in order
  to pool yourself out of the mess
• Take a Random Sampling With Replacement (RSWR)
  and compute statistic T
• Resample M times and recompute statistic T
• Derive Empirical Bootstrap Distribution (EBD)
• EEBD and STDEBD and EBD percentiles estimate
  ET and STDT and Bootstrap Confidence Interval
  for population parameter

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Bootstrap testing of the mean
Hybrid1 2060 2127 1947 2140 1960 1960 2134 2054 20
94 2087 2267 2427 2174 2107 2267 2154 2167 2147 22
14 2160 2180 2220 2167 2174 2280 2187 2180 2060 20
60 2054 2240 2140
Is this significantly different from 2150 ?
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Boot1smp.exe
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RSWR
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Empirical Bootstrap Distribution
X-bar Std 2135.03 87.850 2149.84 121.6
31 2141.19 109.258 2149.09 78.084 2134.00 103.856
2122.13 73.843 2119.66 86.625 2113.59 107.136 2138
.97 101.693 2163.00 67.725
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Empirical Bootstrap Distribution
Empirical Bootstrap Distribution of mean
0.95 conf. BI (2109.5, 2179.9)
EBD of STD
2150
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Bootstrapping the ANOVA
Hybrid1 Hybrid2 Hybrid3 2060 1907 1887 2127 194
0 1834 1947 1700 1587 2140 1934 1814 1960 17
07 1614 1960 1680 1680 2134 1940 1747 2054 1
794 1660 2094 1707 1600
F MSBetween/MSWithin 49.274
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EBD of F values
ANOVTEST.EXE
F 49.274
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Bootstrapping Stress Strength relationships

• Draw samples from X and Y
• X Stress or Load distributions
• Y Strength distribution
• Estimate P( XgtY)

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EBD of P(XgtY)

• X .0352, .0397, .0677, .0233, .0873, .1156,
  .0286, .0200, .0797, .9972, .0245, .0251, .0469,
  .0838, .0796
• Y 1.7700, .9457, 1.8985, 2.6121, 1.0929, .0362,
  1.0615, 2.3895, .0982, .7971, .8316, 3.2304,
  .4373, 2.5648, .6377
• P( XgtY) 0.04 with P.95 0.08