Qu P, Qu Y
Department of Statistics, University of Kentucky, 817 Patterson Office Tower, Lexington, Kentucky 40506-0027, USA.
Biometrics. 2000 Dec;56(4):1249-55. doi: 10.1111/j.0006-341x.2000.01249.x.
After continued treatment with an insecticide, within the population of the susceptible insects, resistant strains will occur. It is important to know whether there are any resistant strains, what the proportions are, and what the median lethal doses are for the insecticide. Lwin and Martin (1989, Biometrics 45, 721-732) propose a probit mixture model and use the EM algorithm to obtain the maximum likelihood estimates for the parameters. This approach has difficulties in estimating the confidence intervals and in testing the number of components. We propose a Bayesian approach to obtaining the credible intervals for the location and scale of the tolerances in each component and for the mixture proportions by using data augmentation and Gibbs sampler. We use Bayes factor for model selection and determining the number of components. We illustrate the method with data published in Lwin and Martin (1989).
在用杀虫剂持续处理后，在易感昆虫群体中会出现抗性品系。了解是否存在任何抗性品系、其比例是多少以及该杀虫剂的半数致死剂量是多少很重要。Lwin和Martin（1989年，《生物统计学》45卷，721 - 732页）提出了一个概率混合模型，并使用期望最大化（EM）算法来获得参数的最大似然估计。这种方法在估计置信区间和检验成分数量方面存在困难。我们提出一种贝叶斯方法，通过使用数据扩充和吉布斯采样器来获得每个成分中耐受性的位置和尺度以及混合比例的可信区间。我们使用贝叶斯因子进行模型选择和确定成分数量。我们用Lwin和Martin（1989年）发表的数据来说明该方法。
