Importance Sampling: Intrinsic Dimension and Computational Cost
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee accurate approximations. Intuitively, some notion of distance...
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| Veröffentlicht in: | Statistical science 2017-08, Vol.32 (3), p.405-431 |
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| container_title | Statistical science |
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| creator | Agapiou, S. Papaspiliopoulos, O. Sanz-Alonso, D. Stuart, A. M. |
| description | The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee accurate approximations. Intuitively, some notion of distance between the target and the proposal should determine the computational cost of the method. A major challenge is to quantify this distance in terms of parameters or statistics that are pertinent for the practitioner. The subject has attracted substantial interest from within a variety of communities. The objective of this paper is to overview and unify the resulting literature by creating an overarching framework. A general theory is presented, with a focus on the use of importance sampling in Bayesian inverse problems and filtering. |
| doi_str_mv | 10.1214/17-STS611 |
| format | Article |
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| ispartof | Statistical science, 2017-08, Vol.32 (3), p.405-431 |
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| language | eng |
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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | Approximation Bayesian analysis Computational efficiency Filtration Importance sampling Independent sample Inverse problems Rational expectations Sampling Statistical analysis Statistical methods Statistics |
| title | Importance Sampling: Intrinsic Dimension and Computational Cost |
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