### Abstract

Estimation of population size has traditionally been viewed from a finite population sampling perspective. Typically, the objective is to obtain an estimate of the total population count of individuals within some region. Often, some stratification scheme is used to estimate counts on subregions, whereby the total count is obtained by aggregation with weights, say, proportional to the areas of the subregions. We offer an alternative to the finite population sampling approach for estimating population size. The method does not require that the subregions on which counts are available form a complete partition of the region of interest. In fact, we envision counts coming from areal units that are small relative to the entire study region and that the total area sampled is a very small proportion of the total study area. In extrapolating to the entire region, we might benefit from assuming that there is spatial structure to the counts. We implement this by modeling the intensity surface as a realization from a spatially correlated random process. In the case of multiple population or species counts, we use the linear model of coregionalization to specify a multivariate process which provides associated intensity surfaces hence association between counts within and across areal units. We illustrate the method of population size estimation with simulated data and with tree counts from a Southwestern pinyon-juniper woodland data set.

Original language | English (US) |
---|---|

Pages (from-to) | 193-205 |

Number of pages | 13 |

Journal | Environmental and Ecological Statistics |

Volume | 14 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- Coregionalization
- Generalized linear model
- Hierarchical model
- Log-linear model
- Model-based geostatistics
- Multivariate spatial random effects

### ASJC Scopus subject areas

- Environmental Science(all)
- Environmental Chemistry

### Cite this

*Environmental and Ecological Statistics*,

*14*(3), 193-205. https://doi.org/10.1007/s10651-007-0021-4

**Hierarchical spatial modeling for estimation of population size.** / Barber, Jarrett J.; Gelfand, Alan E.

Research output: Contribution to journal › Article

*Environmental and Ecological Statistics*, vol. 14, no. 3, pp. 193-205. https://doi.org/10.1007/s10651-007-0021-4

}

TY - JOUR

T1 - Hierarchical spatial modeling for estimation of population size

AU - Barber, Jarrett J.

AU - Gelfand, Alan E.

PY - 2007/9

Y1 - 2007/9

N2 - Estimation of population size has traditionally been viewed from a finite population sampling perspective. Typically, the objective is to obtain an estimate of the total population count of individuals within some region. Often, some stratification scheme is used to estimate counts on subregions, whereby the total count is obtained by aggregation with weights, say, proportional to the areas of the subregions. We offer an alternative to the finite population sampling approach for estimating population size. The method does not require that the subregions on which counts are available form a complete partition of the region of interest. In fact, we envision counts coming from areal units that are small relative to the entire study region and that the total area sampled is a very small proportion of the total study area. In extrapolating to the entire region, we might benefit from assuming that there is spatial structure to the counts. We implement this by modeling the intensity surface as a realization from a spatially correlated random process. In the case of multiple population or species counts, we use the linear model of coregionalization to specify a multivariate process which provides associated intensity surfaces hence association between counts within and across areal units. We illustrate the method of population size estimation with simulated data and with tree counts from a Southwestern pinyon-juniper woodland data set.

AB - Estimation of population size has traditionally been viewed from a finite population sampling perspective. Typically, the objective is to obtain an estimate of the total population count of individuals within some region. Often, some stratification scheme is used to estimate counts on subregions, whereby the total count is obtained by aggregation with weights, say, proportional to the areas of the subregions. We offer an alternative to the finite population sampling approach for estimating population size. The method does not require that the subregions on which counts are available form a complete partition of the region of interest. In fact, we envision counts coming from areal units that are small relative to the entire study region and that the total area sampled is a very small proportion of the total study area. In extrapolating to the entire region, we might benefit from assuming that there is spatial structure to the counts. We implement this by modeling the intensity surface as a realization from a spatially correlated random process. In the case of multiple population or species counts, we use the linear model of coregionalization to specify a multivariate process which provides associated intensity surfaces hence association between counts within and across areal units. We illustrate the method of population size estimation with simulated data and with tree counts from a Southwestern pinyon-juniper woodland data set.

KW - Coregionalization

KW - Generalized linear model

KW - Hierarchical model

KW - Log-linear model

KW - Model-based geostatistics

KW - Multivariate spatial random effects

UR - http://www.scopus.com/inward/record.url?scp=34548045765&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548045765&partnerID=8YFLogxK

U2 - 10.1007/s10651-007-0021-4

DO - 10.1007/s10651-007-0021-4

M3 - Article

AN - SCOPUS:34548045765

VL - 14

SP - 193

EP - 205

JO - Environmental and Ecological Statistics

JF - Environmental and Ecological Statistics

SN - 1352-8505

IS - 3

ER -