?????? (Monte Carlo simulation)

1
Monte Carlo??

1. ??(introduction)
2. ????????(Random number generation)
3. ????????????
4. Monte Carlo???
5. ??Monte Carlo???????

2
Monte Carlo??

• ??? ??
• (Introduction)

1. Monte Carlo??
2. Monte Carlo????
3. Monte Carlo?????
4. Monte Carlo?????????

3
1.Monte Carlo??

• Monte Carlo??

????????(statistical simulation method)
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4
1.Monte Carlo??

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5
Monte Carlo??

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• (Introduction)

1. Monte Carlo??
2. Monte Carlo????
3. Monte Carlo?????
4. Monte Carlo?????????

6
2.Monte Carlo????
Buffon????
1768?,?????Comte de Buffon???????????
7
2.Monte Carlo????
Problem of Buffons needle
If a needle of length l is dropped at random on
the middle of a horizontal surface ruled with
parallel lines a distance d gt l apart, what is
the probability that the needle will cross one of
the lines?
8
2.Monte Carlo????
Solution

• The positioning of the needle relative to nearby
  lines can be described with a random vector which
  has components

• The random vector is uniformly distributed on the
  region 0,d)0,?). Accordingly, it has
  probability density function 1/d?.

• The probability that the needle will cross one of
  the lines is given by the integral

9
2.Monte Carlo????
Enrico Fermi

• 1930?,??Monte Carlo?????????

• ??????Monte Carlo????,Fermiac,?????????????

10
2.Monte Carlo????
Stanislaw Ulam (1909-1984)
S. Ulam is credited as the inventor of Monte
Carlo method in 1940s, which solves mathematical
problems using statistical sampling.
11
2.Monte Carlo????
Nicholas Metropolis (1915-1999)
The algorithm by Metropolis (and A Rosenbluth, M
Rosenbluth, A Teller and E Teller, 1953) has been
cited as among the top 10 algorithms having the
"greatest influence on the development and
practice of science and engineering in the 20th
century."
12
2.Monte Carlo????
The Name of the Game
Metropolis coined the name Monte Carlo, from
its gambling Casino.
Monte-Carlo, Monaco
13
Monte Carlo??

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• (Introduction)

1. Monte Carlo??
2. Monte Carlo????
3. Monte Carlo?????
4. Monte Carlo?????????

14
3.Monte Carlo?????
Monte Carlo?????
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15
3.Monte Carlo?????
Monte Carlo???????????
16
3.Monte Carlo?????
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17
Monte Carlo??

• ??? ??
• (Introduction)

1. Monte Carlo??
2. Monte Carlo????
3. Monte Carlo?????
4. Monte Carlo?????????

18
4.Monte Carlo?????????
Monte Carlo?????

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4.Monte Carlo?????????
Monte Carlo?????????

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20
4.Monte Carlo?????????

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