Imaging from Interofermetric Data by Bayesian Modeling

据了解，以统计数学研究所目前的计算能力，严格应用基于贝叶斯建模和极大似然方法的技术实现的数据分析是很困难的。然后，我们决定推迟应用统计上最合适的处理技术，直到有了更快的计算机，并将我们的目标转移到准备一个信息准则，以比较传统标准图像形成技术得到的结果和一旦克服了计算成本的困难就会得到的结果。提出了一种新的无估计量信息准则WIC的思想。WIC的研究表明，各种模型拟合方法的性能都可以与极大似然方法进行比较。研究还发现，利用WIC可以实现传统数据处理方法参数的最优调整，从而获得统计可靠的结果。WIC测试和证明有效的情况如下：1。CATDAP模型解释变量的选择。CATDAP模型是列联表数据分析的标准模型。AR模型的订单选择。AR模型是时间序列数据分析的标准模型。多项式回归模型的阶数选择，以及惩罚最小二乘法惩罚权值的选择。结果表明，多项式拟合方法的结果与惩罚最小二乘法的结果可以在同一基上进行比较。控制图像形成的CLEAN方法。我们可以通过最小化WIC值来选择CLEAN方法的最优迭代次数。

It was revealed that, with the present computing power of the Institute of Statistical Mathematics, it is difficult to carry out the data analysis realized by the strict application of the techniques based on Bayesian modeling and the maximum likelihood method.Then, we decided to postpone the application of statistically most appropriate processing technique until a faster computer is available, and shifted our aim to the preparation of an information criterion to compare the results obtained by traditional standard image formation techniques and results which would be obtained once the difficulty about the computing cost would be overcame.We got the idea of WIC, a new estimator-free information criterion. The study of WIC showed that performance of various model fitting methods can be compared with that of the maximum likelihood method. It is also found that with the use of WIC, it is possible to realize the optimum adjustment of parameters of traditional data processing methods, and consequently enable to obtain statistically reliable results.The situations in which WIC was tested and proved effective were as follows :1. Choice of explanatory variables of CATDAP model. CATDAP model is standard model for the contingency table data analysis.2. Order selection of AR model. AR model is a standard model for the time series data analysis.3. Order selection of the polynomial regression model, and the choice of the penalty weight of penalized least squares method. It is shown that the results by the polynomial fitting method and the results by the penalized least squares method can be compared on the same base.4. Control of CLEAN method of image formation. We can choose the optimal iteration count of the CLEAN method by minimizing WIC value.