Markov Chain Monte Carlo: Innovations and Applications, Vol. 7

Glossary

Contributors to this volume come from several different fields, each with their own preferred terminology, which can often overlap. To aid the reader, we have therefore assembled the following glossary of terms and brief definitions, which we have organized under the titles of Probability, Statistical Physics, and Mathematical Genetics.

1. Probability

  • Bernoulli distribution: A random variable X has a Bernoulli distribution if it has probability p of being equal to 1, probability 1 ? p of being equal to ?1.

  • coalescence: A family of random processes X, Y, Z, are said to coalesce if there is some random time T (the coalescence time) at which they are all equal: X(T)=Y(T)=Z(T)= . Sometimes called grand coupling, since two processes X, Y are said to couple if X(T)=Y(T) for some random time T.

  • conditional probability: The conditional probability [AB] of A given B is the ratio [ A and B]/ [B] of the probability of both A and B to the probability of B.

  • coupling technique: The technique of constructing two random processes X and Y such that (a) individually both X and Y have specified statistical behaviour, but (b) the joint behaviour of X and Y meets some useful requirement (perhaps X always lies below Y, or perhaps X and Y couple with X(T)=Y(T)

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