Random Number Generation - University of Michigan
[Pages:43]Random Number Generation
Biostatistics 615/815 Lecture 14
Homework 5, Question 1: Quick Sort Optimization ...
12
200
Thousands
Comparisons
10
167
Time (ms)
8
133
6
100
0
10
20
30
40
50
60
M
Homework 5, Question 1: Merge-Sort Optimization
14
200
Thousands
Comparisons
Time (ms)
175 12
150
10 125
8
100
0
10
20
30
40
50
60
M
Homework 5, Question 2:
z Comparison of Hashing Strategies
? Linear hashing ? Double hashing
z Interesting aspects:
? Memory dramatically impacts performance ? In double-hashing, it is important to choose the
second hash function carefully:
? Specifically, it is key to avoid that it might return the
values 0, 1 and any multiple of the table size M
Today
z Random Number Generators
? Key ingredient of statistical computing
z Discuss properties and defects of alternative generators
Some Uses of Random Numbers
z Simulating data
? Evaluate statistical procedures ? Evaluate study designs ? Evaluate program implementations
z Controlling stochastic processes
? Markov-Chain Monte-Carlo methods
z Selecting questions for exams
Random Numbers and Computers
z Most modern computers do not generate truly random sequences
z Instead, they can be programmed to produce pseudo-random sequences
? These will behave the same as random
sequences for a wide-variety of applications
Uniform Deviates
z Fall within specific interval (usually 0..1) z Potential outcomes have equal probability
z Usually, one or more of these deviates are used to generate other types of random numbers
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