英语翻译The MCMC method [10] is used to simulate the posterior d

英语翻译
The MCMC method [10] is used to simulate the posterior distributions of interest.In each case,we perform the Metropolis–Hasting’s algorithm [see [12,13]] by using log-normal as the proposal distribution for the parameters to simulate a sequence of 100,000 random variates iteratively by discarding the first 1000 iterations and then choosing one sample point in every 100 iterations to reduce the correlation between the iterated samples.A sample of size 990 is thus obtained to approximate the posterior distribution of (α0,α1).Table 2 presents the results on the estimates of α0 and α1 corresponding to the three priors for the three choices of (α0,α1).Since we expect the results to rely more on priors when the data give less information,we increased the value of c2 as the failure rate decreased.We observe from Table 2 that the estimates of the parameters are all very good for specified c2 in each data set.In the first case,about half the data survived at observation times,and the estimates in this case are quite close for all three priors with moderate confidence on the prior accuracy.In the second case in which the survival data are less than 20%,with c2 = 0.001,the Bayes estimates with respect to the prior π1 are not as good as the other two.When the failure rate is nearly zero with extremely accurate prior beliefs on pij as in the last case considered,π1 again is not as accurate as the other two.These reveal that the exponential priors on α0 and α1 seem to lose some information contained in pij possibly due to the additional error caused by the least-squares estimation in finding the hyperparameters.It is also seen that the prior π2 yields the smallest posterior standard errors for the estimates,while the prior π1 results in the largest standard errors for the estimates.

这个推理方法[10]是用来模拟后分布的兴趣.在每种情况下,我们完成了Metropolis-Hasting的算法(参见[12、13]]的使用服从对数正态分布的提案的参数来模拟随机变量序列的迭代离开10第1000迭代,然后选择一个采样点在每100个迭代来减少迭代关系样品.一个样本的大小是获得近似990后验概率(α0,α1).表2提出的估计结果,α1α0相对应的三个选择三种先验的,α1(α0).因为我们期望的结果时,更多的依靠先验信息的数据,我们增加少的价值下降的失败率不便…从表2,我们观察到的参数估计都是很好的,在每个数据集指定c2).在第一个案例中,约有半数的数据,在观察次幸存下来的估计,在这种情况下都很近,三个人的信心与适度的先验先验精度.在第二种情形中生存的数据是少于20%,c2 = 0.001、贝叶斯估计的π1之前就不如其他两种.当失败率是几乎为零和精确的之前的信念pij如上一例认为,π1又不准确.这些显示了在α0和α1指数先验似乎损失了一些信息在pij可能由于附加误差最小二乘估计在寻找hyperparameters.它也看到了π2前收益最小误差估计的后路标准,而之前的π1结果中最大的错误的估计为标准.