## Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling (1997)

Citations: | 146 - 4 self |

### BibTeX

@MISC{Gelman97simulatingnormalizing,

author = {Andrew Gelman and Xiao-Li Meng},

title = {Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling},

year = {1997}

}

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### OpenURL

### Abstract

Computing (ratios of) normalizing constants of probability models is a fundamental computational problem for many statistical and scientific studies. Monte Carlo simulation is an effective technique, especially with complex and high-dimensional models. This paper aims to bring to the attention of general statistical audiences of some effective methods originating from theoretical physics and at the same time to explore these methods from a more statistical perspective, through establishing theoretical connections and illustrating their uses with statistical problems. We show that the acceptance ratio method and thermodynamic integration are natural generalizations of importance sampling, which is most familiar to statistical audiences. The former generalizes importance sampling through the use of a single "bridge" density and is thus a case of bridge sampling in the sense of Meng and Wong (1996). Thermodynamic integration, which is also known in the numerical analysis literature as Oga...