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Metropolis algorithm does not necessary require symmetric trial proposal probability. While typical canonical ensemble moves may happen to be symmetric for simplicity, biased methods and grand canonical insertion and deletion of particles are not. Thus, Metropolis algorithm does not require this. See 'Understanding molecular simulation' by Frenkel and Smit. The title of this section has (symmetric proposal...) which correctly indicates this discussion only applies to the symmetric case. |
InfCompact (talk | contribs) m →Use in numerical integration: Can't integrate arbitrary functions, rather only measurable functions. |
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: <math>P(E) = \int_\Omega A(x) P(x) \,dx,</math>
where <math>A(x)</math> is
For example, consider a [[statistic]] <math>E(x)</math> and its probability distribution <math>P(E)</math>, which is a [[marginal distribution]]. Suppose that the goal is to estimate <math>P(E)</math> for <math>E</math> on the tail of <math>P(E)</math>. Formally, <math>P(E)</math> can be written as
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