In this paper, we consider some objective priors for the ratio of variabilities in a bivariate normal distribution. We develop the first and second order matching priors and reference priors. We obtain that the second order matching prior matches the alternative coverage probabilities up to the same order. It is also an HPD matching priors. It turns out that the derived reference priors do not satisfy a second order matching criterion. The simulation result shows that the second order matching prior performs better than reference priors based on matching the target coverage probabilities in a frequentist sense. Finally, we show that the second order matching prior and reference priors produce confidence sets with an expected length shorter than the Cox and Reid adjustment.

在本文中，我们考虑了二元正态分布中变异率的一些客观先验。我们开发一阶和二阶匹配先验和参考先验。我们获得第二个先验匹配先验匹配替代覆盖率的概率，直到相同的阶次。这也是HPD匹配的先验条件。事实证明，导出的参考先验不满足二阶匹配标准。仿真结果表明，基于频域意义上的目标覆盖概率匹配，二阶匹配先验比参考先验具有更好的性能。最后，我们表明二阶匹配先验和参考先验产生的置信度集的预期长度比Cox和Reid调整短。