Objective Bayesian analysis of zero-and-one-inflated geometric distribution
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摘要: 在医疗卫生、金融证券等应用领域，经常会同时出现零观测值、一观测值较多的情况. 为更好地拟合这类数据，提出0–1膨胀几何分布模型并进行客观贝叶斯分析. 通过参数变换，得到Jeffreys先验和reference先验. 设计后验分布的抽样算法，设置不同的样本量和参数真值，采用数值模拟方法对不同客观先验下的估计效果进行评估.
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关键词:
- 0–1膨胀几何分布 /
- Jeffreys先验 /
- reference先验 /
- 客观贝叶斯分析
Abstract: Count datas with excess zeros and ones arise frequently in various fields such as medical health, finance and securities. In order to fit these datas better, a zero-and-one-inflated geometric distribution model was proposed and the objective Bayesian analysis was carried out. Based on parameter transformation, the Jeffreys prior and the reference prior were derived for this model. For different sample size and different true values of the parameters, simulations were adopted to assess the performance under the different objective priors through the sampling algorithm. -
表 1
$\theta = 0.8$ 下参数估计量的均值Table 1. Mean of parameter estimators when
$\theta = 0.8$ ${q_1}$ ${q_2}$ $n$ ${\theta _J}$ ${q_{1J}}$ ${q_{2J}}$ ${\theta _{R1}}$ ${q_{1R1}}$ ${q_{2R1}}$ ${\theta _{R2}}$ ${q_{1R2}}$ ${q_{2R2}}$ 0.3 0.4 20 0.768 0.283 0.357 0.783 0.289 0.361 0.792 0.288 0.362 50 0.779 0.284 0.374 0.787 0.291 0.388 0.793 0.289 0.387 0.6 20 0.776 0.282 0.504 0.785 0.290 0.556 0.788 0.290 0.555 50 0.781 0.287 0.584 0.791 0.302 0.592 0.792 0.298 0.594 0.7 0.4 20 0.772 0.669 0.347 0.786 0.672 0.373 0.790 0.671 0.376 50 0.787 0.685 0.376 0.792 0.694 0.388 0.794 0.693 0.386 0.6 20 0.775 0.724 0.545 0.784 0.724 0.575 0.789 0.723 0.581 50 0.791 0.721 0.569 0.793 0.716 0.594 0.795 0.715 0.593 
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表 2
$\theta = 0.8$ 下参数估计量的均方误差Table 2. Mean squared error of parameter estimators when
$\theta = 0.8$ ${q_1}$ ${q_2}$ $n$ ${\theta _J}$ ${q_{1J}}$ ${q_{2J}}$ ${\theta _{R1}}$ ${q_{1R1}}$ ${q_{2R1}}$ ${\theta _{R2}}$ ${q_{1R2}}$ ${q_{2R2}}$ 0.3 0.4 20 0.083 0.074 0.098 0.081 0.072 0.088 0.079 0.072 0.087 50 0.065 0.037 0.085 0.062 0.033 0.075 0.061 0.034 0.075 0.6 20 0.076 0.072 0.093 0.078 0.062 0.092 0.075 0.063 0.091 50 0.061 0.036 0.072 0.058 0.024 0.063 0.055 0.026 0.062 0.7 0.4 20 0.087 0.045 0.096 0.086 0.041 0.086 0.084 0.042 0.084 50 0.056 0.038 0.074 0.066 0.032 0.073 0.061 0.035 0.072 0.6 20 0.065 0.037 0.083 0.072 0.031 0.082 0.069 0.032 0.081 50 0.057 0.035 0.078 0.056 0.026 0.072 0.045 0.028 0.072
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