2007 Fiscal Year Final Research Report Summary
Study of time-space modeling using mixture model
| Project/Area Number |
16500179
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Sapporo Gakuin University |
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Principal Investigator |
NAKAMURA Nagatomo Sapporo Gakuin University, Dept of Economics, Professor (70207900)
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| Project Period (FY) |
2004 – 2007
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| Keywords | Mixture Model / Non Ignorable Missing / Plasma Velocity Data / Geotail Space Craft |
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| Research Abstract |
The aim of this research is integrated analysis of plasma velocity data. This dataset contains some difficult problems in statistical meaning, there are : i) raw data consists of pseudo-counting and unequal interval measurement in velocity space, ii) the data is assumed to arise some populations, and iii) measurement space have missing regions or un-observable area which is non-ignorable. Especially, this study concentrates second and third problems, the details are as follows.
A dataset that contains missing regions is assumed to arise from two or more populations. In order to decompose the data into meaningful component distributions, a normal mixture model can be applied. A problem with this approach is that the estimated parameters are biased by fitting the standard normal mixture model. To collect the bias, a log-likelihood function for missing region probabilities is constructed, and the maximum likelihood estimators of the parameters-i.e. mixing proportions, mean vectors, and variance-covariance matrixes-are derived in the context of the EM algorithm. The performance of the model is verified by numerical experiments, and the model is applied to plasma velocity data.
The remaining problem is that one of some mass-plasma appear and/or disappear in the series, statistical models which are time-independent and time-series models should be constructed in future.
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