| Project/Area Number |
63540183
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
ISHIGURO Makio The Institute of Statistical Mathematics, Associate Professor, 予測制御研究系, 助教授 (10000217)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIGURO Masato National Astronomical Observatory, Professor, 電波天文学研究系, 教授 (40023684)
TANABE Kunio The Institute of Statistical Mathematics, Professor, 予測制御研究系, 教授 (50000203)
KASHIWAGI Nobuhisa The Institute of Statistical Mathematics, Assistant Professor, 調査実験解析研究系, 助手 (50150032)
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| Project Period (FY) |
1988 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1990: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1989: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1988: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | 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 |
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| Research Abstract |
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.
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