## Discovery Sampling And Selection Models (1994)

Venue: | In Decision Theory and Related Topics |

Citations: | 5 - 2 self |

### BibTeX

@INPROCEEDINGS{West94discoverysampling,

author = {Mike West},

title = {Discovery Sampling And Selection Models},

booktitle = {In Decision Theory and Related Topics},

year = {1994},

pages = {221--235},

publisher = {Springer Verlag}

}

### OpenURL

### Abstract

Various aspects of Bayesian inference in selection and size biased sampling problems are presented, beginning with discussion of general problems of inference in infinite and finite populations subject to selection sampling. Estimation of the size of finite populations and inference about superpopulation distributions when sampling is apparently informative is then developed in two specific problems. The first is a simple example of truncated data analysis, and some details of simulation based Bayesian analysis are presented. The second concerns discovery sampling in which units of a finite population are selected with probabilities proportional to some measure of size. A well-known area of application is in the discovery of oil reserves, and some recently published data from this area is analysed here. Solutions to the computational problems arising are developed using iterative simulation methods. Finally, some comments are made on extensions, including multiparameter superpopulation...

### Citations

549 |
The calculation of posterior distributions by data augmentation
- Tanner, Wong
- 1987
(Show Context)
Citation Context ...ve posterior simulation schemes (Gelfand and Smith, 1990) allow trivial coding of routines to simulate posterior distributions in certain common selection models. General issues of data augmentation (=-=Tanner and Wong, 1987-=-) and of dealing with truncation and censoring (Kuo and Smith, 1992) in simulation analyses are particularly relevant. Suppose the known selection function w(y) 0 is a cumulative distribution function... |

397 | Bayesian density estimation and inference using mixtures
- Escobar, West
- 1995
(Show Context)
Citation Context ...lements of Y nD but with this corrected underlying log-normal distribution. (d) Nonparametric superpopulation models Gibbs sampling approaches to data analysis using Dirichlet process mixture models (=-=Escobar and West, 1992-=-) naturally lends itself to the current context. Assume, for example, that the superpopulation distribution is modelled as a mixture of log-normal distributions. The developments in Escobar and West s... |

373 |
Sampling based approaches to calculating marginal densities
- Gelfand, Smith
- 1990
(Show Context)
Citation Context ...clude regression of the observed y values on independent variables, leading to higher dimensional parameters through the introduction of regression parameters. Iterative posterior simulation schemes (=-=Gelfand and Smith, 1990-=-) allow trivial coding of routines to simulate posterior distributions in certain common selection models. General issues of data augmentation (Tanner and Wong, 1987) and of dealing with truncation an... |

96 | How many iterations in the Gibbs sampler
- Raftery, Lewis
- 1992
(Show Context)
Citation Context ... of r and `, draw a random sample of size N \Gamma n from the distribution with density (4) to produce a revised Y nD; (e) proceed to (b), and iterate. After `burning-in' for some initial iterations (=-=Raftery and Lewis, 1992-=-), subsequent samples will approximate draws from the joint posterior determined by these conditionals, with margins p(`jD), p(Y nDjD), p(tjD), etc. Note that both parametric and predictive inference ... |

15 |
Bayesian computations in survival models via the Gibbs sampler
- Kuo, Smith
- 1992
(Show Context)
Citation Context ...al coding of routines to simulate posterior distributions in certain common selection models. General issues of data augmentation (Tanner and Wong, 1987) and of dealing with truncation and censoring (=-=Kuo and Smith, 1992-=-) in simulation analyses are particularly relevant. Suppose the known selection function w(y)s0 is a cumulative distribution function (or may be standardised to become one), such as in the common trun... |

13 | Bayesian analysis of selection models
- Bayarri, DeGroot
- 1987
(Show Context)
Citation Context ...gative weight or selection function that biases sampling relative to the underlying distribution. Truncation to a known set A via the indicator selection function w(y) = I(y 2 A) is a common example (=-=Bayarri and DeGroot, 1987-=-). The term c(`) is a normalising constant for the density of selected sample values. Inference about `, which may be analytically straightforward under the original model f(yj`), is usually more comp... |

4 | Maximum likelihood estimation under a successive sampling discovery model - Nair, Wang - 1989 |

3 | Estimating the size of a truncated sample - Sanathanan - 1977 |

1 |
Information is sampling rules
- Irony
- 1992
(Show Context)
Citation Context ...ribution function (or may be standardised to become one), such as in the common truncation example where w(y) = 0 for y ! a and w(y) = 1 for ysa for some fixed threshold a (Bayarri and DeGroot, 1987; =-=Irony, 1992-=-). In such cases, a single observationsy can be modelled as arising as follows: a random sequence x 1 ; x 2 ; : : : ; is generated from f(:j`) and values are accepted with probabilities proportional t... |

1 | A Bayesian analysis of a discovery sampling model. ISDS discussion paper - Morrison, West - 1992 |