@article{eve-18-aa-mtcarlo,
  author = {Richard G. Everitt},
  title = {Efficient Importance Sampling in Low Dimensions Using Affine Arithmetic},
  journal = {Computational Statistics},
  volume = {33},
  pages = {1--29},
  year = 2018,
  month = may,
  doi = {10.1007/s00180-017-0729-z},
  comment = {Uses affine arithmetic to better enclose a function in order to do Monte Carlo estimation.},
  abstract = {Despite the development of sophisticated techniques such as sequential Monte Carlo (Del Moral et al. in J R Stat Soc Ser B 68(3):411--436, 2006), importance sampling (IS) remains an important Monte Carlo method for low dimensional target distributions (Chopin and Ridgway in Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation, 32:64--87, 2017). This paper describes a new technique for constructing proposal distributions for IS, using affine arithmetic (de Figueiredo and Stolfi in Numer Algorithms 37(1--4):147--158, 2004). This work builds on the Moore rejection sampler (Sainudiin in Machine interval experiments, Cornell University, Ithaca, 2005; Sainudiin and York in Algorithms Mol Biol 4(1):1, 2009) to which we provide a comparison.}
}