TY - JOUR

T1 - Markov Chain Monte Carlo on optimal adaptive sampling selections

AU - Chao, Chang Tai

N1 - Funding Information:
Support for this research was provided by the National Institutes of Health, National Institute on Drug Abuse (RO1 DA09872) and the National Sciences Foundation (DMS-9626102). The author thanks his advisor, who is the P.I. of both research grants, for his guidance during this research. The author also thanks Cindy A. Werner for the use of her data. Her work is supported by the National Geographic Society (Grant No. 5997-97) and a NASA/STIR program at The Pennsylvania State University.

PY - 2003/3

Y1 - 2003/3

N2 - Under a Bayesian population model with a given prior distribution, the optimal sampling strategy with a fixed sample size n is an n-phase adaptive one. That is, the selection of the next sampling units should sequentially depend on the information obtained from the previously selected units, including the observed values of interest. Such an optimal strategy is in general not executable in practice due to its intensive computation. In many survey sampling situations, an important problem is that one would like to select a set of units in addition to a certain number of sampling units which have been observed. If the optimal strategy is an adaptive one, the selection of the additional units should take both the labels and the observed values of the already selected units into account. Hence, a simpler optimal two-phase adaptive sampling strategy under a Bayesian population model is proposed in this article for practical interest. A Markov chain Monte Carlo method is used to approximate the posterior joint distribution of the unobserved population units after the first phase sampling, for the optimal selection of the second phase sample. This approximation method is found to be successful to select the optimal second-phase sample. Finally, this optimal strategy is applied to a set of data from a study of geothermal CO2 emissions in Yellowstone National Park as a practical illustrative example.

AB - Under a Bayesian population model with a given prior distribution, the optimal sampling strategy with a fixed sample size n is an n-phase adaptive one. That is, the selection of the next sampling units should sequentially depend on the information obtained from the previously selected units, including the observed values of interest. Such an optimal strategy is in general not executable in practice due to its intensive computation. In many survey sampling situations, an important problem is that one would like to select a set of units in addition to a certain number of sampling units which have been observed. If the optimal strategy is an adaptive one, the selection of the additional units should take both the labels and the observed values of the already selected units into account. Hence, a simpler optimal two-phase adaptive sampling strategy under a Bayesian population model is proposed in this article for practical interest. A Markov chain Monte Carlo method is used to approximate the posterior joint distribution of the unobserved population units after the first phase sampling, for the optimal selection of the second phase sample. This approximation method is found to be successful to select the optimal second-phase sample. Finally, this optimal strategy is applied to a set of data from a study of geothermal CO2 emissions in Yellowstone National Park as a practical illustrative example.

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U2 - 10.1023/A:1021993627070

DO - 10.1023/A:1021993627070

M3 - Article

AN - SCOPUS:0037340804

SN - 1352-8505

VL - 10

SP - 129

EP - 151

JO - Environmental and Ecological Statistics

JF - Environmental and Ecological Statistics

IS - 1

ER -