Python Programming for Biology: Bioinformatics and Beyond

The Monte Carlo method

The Monte Carlo method

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means to randomly test data points to approximate or guess a

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solution,  thus  getting  a  good  idea  of  what  is  going  on  by  sampling  only  a  few  points,

rather than many. This approach is often coupled with targeting the selection of data points

towards the most promising or important results. This leads directly into the Markov chain

idea, where we can base a new selection on the last one, and a famous implementation of

this is the Metropolis-Hastings algorithm,

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,

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for making the next guess, for an effectively

random walk with probabilistic selection that echoes thermodynamic energy.

Key to the implementation of Monte Carlo and related methods is the ability to generate

random,  or  almost  random,  numbers.  Fortunately  in  Python  we  can  exploit  the  random

module  and  its  equivalent  in  NumPy.  Usually  we  do  not  require  absolutely  random

numbers so the usual pseudorandom generators will be sufficient. The important thing is

that  the  distribution  of  the  emitted  numbers  is  approximately  correct  (typically  uniform;

level  throughout  a  range)  and  that  there  is  no  significant  selection  bias.  Having  truly

random  numbers  that  are  entirely  unpredictable  doesn’t  matter.  Indeed,  being  able  to

restart a Monte Carlo run with the same set of pseudorandom numbers can be useful for

testing.