标题： 一种针对零膨胀幂级数分布中过多零值的贝叶斯检验 显示英文标题

标题： A Bayesian test for excess zeros in a zero-inflated power series distribution

摘要： 幂级数分布是一个有用的单参数离散指数族的子类，适用于对计数数据进行建模。 一个零膨胀的幂级数分布是幂级数分布和在零处退化分布的混合，其中退化分布的混合概率为$p$。 这种分布适用于可能有额外零值的计数数据。 一个问题在于该混合模型是否可以简化为幂级数部分，对应于$p=0$，或者数据中是否有如此多的零值，以至于相对于纯幂级数分布必须在模型中包含零膨胀，即$p\geq0$。 这个问题很难，部分原因是$p=0$是一个边界点。 在这里，我们提出了一种基于识别参数空间可以扩展以允许$p$为负数的贝叶斯检验。 然而，$p$的负值与将$p$解释为混合概率不一致，但它们索引的分布在物理上和概率上是有意义的。 我们将我们的贝叶斯解法与两种标准的频率论检验过程进行比较，发现在样本量$n$和参数值最重要的范围内，使用后验概率作为检验统计量在模拟中比得分检验和似然比检验具有稍高的功效。我们的方法在三个实际数据集上也表现良好。 显示英文摘要

摘要： Power series distributions form a useful subclass of one-parameter discrete exponential families suitable for modeling count data. A zero-inflated power series distribution is a mixture of a power series distribution and a degenerate distribution at zero, with a mixing probability $p$ for the degenerate distribution. This distribution is useful for modeling count data that may have extra zeros. One question is whether the mixture model can be reduced to the power series portion, corresponding to $p=0$, or whether there are so many zeros in the data that zero inflation relative to the pure power series distribution must be included in the model i.e., $p\geq0$. The problem is difficult partially because $p=0$ is a boundary point. Here, we present a Bayesian test for this problem based on recognizing that the parameter space can be expanded to allow $p$ to be negative. Negative values of $p$ are inconsistent with the interpretation of $p$ as a mixing probability, however, they index distributions that are physically and probabilistically meaningful. We compare our Bayesian solution to two standard frequentist testing procedures and find that using a posterior probability as a test statistic has slightly higher power on the most important ranges of the sample size $n$ and parameter values than the score test and likelihood ratio test in simulations. Our method also performs well on three real data sets.