Monte Carlo methods

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Monte Carlo methods

• Mike Sinclair

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Overview

• Monte Carlo
• Based on roulette wheel probabilities
• Used to describe large-scale interactions in
  biology and physics
• Especially useful for solving differential and
  integral calculus problems
• Uses a random number generator and random walks

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Example problem

• Attempt to find p
• Random walk find ratio of points within the
  circle vs. entire unit square
• Time-step
• Expectation Enough steps and ratio approaches p

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Another problem

• Integrating sin (1/x)2 is extremely difficult,
  but . . .
• . . . a Monte Carlo approach yields a value
  0.667.

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Approach

• Monte Carlo methods use lots and lots of random
  steps . . .
• . . . and usually compares values within a
  function to the total trials
• Although simple to design, may take lots and lots
  of time!

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Conclusions

• Monte Carlo methods are used extensively in
  biology and physics.
• It uses a combination of random walk and a ratio
  test.
• It can be visualized by a modeling large numbers
  of particles.
• Slow but very effective for studying complex
  systems.