## Advances in Applied Probability

- Adv. in Appl. Probab.
- Volume 40, Number 2 (2008), 293-601

### Importance sampling and the two-locus model with subdivided population structure

Robert C. Griffiths, Paul A. Jenkins, and Yun S. Song

#### Abstract

The diffusion-generator approximation technique developed by De Iorio and Griffiths (2004a) is a very useful method of constructing importance-sampling proposal distributions. Being based on general mathematical principles, the method can be applied to various models in population genetics. In this paper we extend the technique to the neutral coalescent model with recombination, thus obtaining novel sampling distributions for the two-locus model. We consider the case with subdivided population structure, as well as the classic case with only a single population. In the latter case we also consider the importance-sampling proposal distributions suggested by Fearnhead and Donnelly (2001), and show that their two-locus distributions generally differ from ours. In the case of the infinitely-many-alleles model, our approximate sampling distributions are shown to be generally closer to the true distributions than are Fearnhead and Donnelly's.

#### Article information

**Source**

Adv. in Appl. Probab. Volume 40, Number 2 (2008), 473-500.

**Dates**

First available: 1 July 2008

**Permanent link to this document**

http://projecteuclid.org/euclid.aap/1214950213

**Digital Object Identifier**

doi:10.1239/aap/1214950213

**Mathematical Reviews number (MathSciNet)**

MR2433706

**Zentralblatt MATH identifier**

1144.62092

**Subjects**

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Secondary: 93E25: Other computational methods 92D15: Problems related to evolution

**Keywords**

Coalescent process recombination diffusion process importance sampling migration subdivided population

#### Citation

Griffiths, Robert C.; Jenkins, Paul A.; Song, Yun S. Importance sampling and the two-locus model with subdivided population structure. Advances in Applied Probability 40 (2008), no. 2, 473--500. doi:10.1239/aap/1214950213. http://projecteuclid.org/euclid.aap/1214950213.