Imaging from Interofermetric Data by Bayesian Modeling

通过贝叶斯建模对 Interofermetric 数据进行成像

• 批准号: 63540183
• 负责人: ISHIGURO Makio
• 金额: $ 1.47万
• 依托单位: The Institute of Statistical Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63540183/
• 关键词: Interferometric data; Information Criterion; WIC; AIC; Maximum likelihood method; Bayesian Modeling; 量尤推定法; 電波天文学; 統計的モデル; セルフキャリブレ-ション; CLEAN法; ベイズモデル; 統計的データ解析; ABIC; セルフキャリブレーション; 事前情報; 画像形成

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.

结果显示，以统计数学研究所目前的计算能力，很难进行严格应用基于贝叶斯建模和最大似然法的技术实现的数据分析，因此决定推迟应用统计学上最合适的处理技术，直到有更快的计算机可用，并将目标转移到准备一个信息准则上，将传统的标准成像技术所得到的结果与一旦克服了计算代价的困难所得到的结果进行比较，从而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可以与最大似然法进行比较。同时发现，利用WIC可以实现对传统数据处理方法参数的优化调整，从而得到统计上可靠的结果。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模型的阶次选择。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，惩罚最小二乘法惩罚权的选择。结果表明，多项式拟合法和惩罚最小二乘法的结果可以在相同的基础上进行比较.图像形成的CLEAN方法的控制。我们可以通过最小化WIC值来选择CLEAN方法的最佳迭代次数。

项目成果

Ishiguro, M: "Interfermetric data analysis" Proceedings of the Institute of Statistical Mathematics. Vol. 38. (1991)

Ishiguro, M：“干涉数据分析”统计数学研究所论文集。

Ishiguro M.,Akaike H.: "DALL:Davidois Algorithm for Log Litcelihood MaximizationーA FORTRAN subroutine for Statistical Model BuitdersーComputer Science Monographs No25" The Iustitute of Statistical Mathematies,

Ishiguro M.，Akaike H.：“DALL:Davidois Algorithm for Log Litcelihood Maximization-A FORTRAN subroutine for Statistical Model Buitders-Computer Science Monographs No25” 统计数学研究所，

Ishiguro M.,Sakamoto Y.: "WIC:An EstimatorーFree Information Criterion" Anads of The Institute of Statistical Mathematirs.

Ishiguro M.、Sakamoto Y.：“WIC：无估计器信息准则”统计数学家研究所的 Anads。

石黒 真木夫: "電波望遠鏡デ-タ解析" 統計数理. 38. (1991)

Makio Ishiguro：“射电望远镜数据分析”统计数学38。（1991）

Ishiguro,M.,Sakamoto,Y.: "WIC:An EstimatorーFree Information Criterion" Anals of The Institute of Statistical Mathematics.

Ishiguro, M.，Sakamoto, Y.：“WIC：无估计量信息准则”统计数学研究所年鉴。