2002 Fiscal Year Final Research Report Summary
Constructions of array type block designs and their statistical optimality and efficiency
| Project/Area Number |
12640140
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Keio University |
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Principal Investigator |
JIMBO Masakazu Keio University, Dept. Math., Professor, 理工学部, 教授 (50103049)
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| Co-Investigator(Kenkyū-buntansha) |
KURIKI Shinji Osaka Pref. University, Associate Prof., 工学部, 助教授 (00167389)
SHIMIZU Kunio Keio University, Dept. Math., Professor, 理工学部, 教授 (60110946)
SHIBATA Ritei Keio University, Dept. Math., Professor, 理工学部, 教授 (60089828)
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| Project Period (FY) |
2000 – 2002
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| Keywords | split-block design / BISBD / optimality / efficiency factor / BIBD with nested row and columns / grid design / DNA library screening / pooling design |
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| Research Abstract |
In this research, we investigate combinatorial constructions and statistical optimality, efficiency of array type block designs such as a split-block design, BIB design with nested rows and columns, or grid designs. In planning such design, it is important to consider the optimality and efficiency. We showed that if a balanced incomplete split-block design is utilized, it is optimal to estimate the interaction effects. And we gave some constructions of such designs. Moreover, we obtain combinatorial characterization that the efficiency factor of a design can be obtained explicitly.
On the other hand, we showed that a grid block design can be applied to a DNA library screening as an efficient way of group testing. And some constructions of a grid design was obtained.
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