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大規模なこと Large scale
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均一分布 Uniform distribution
X<-runif(N) plot(X) plot(sort(X)) plot(ppoints(N,a=0),sort(X))
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均一分布からのk個の乱数の最小値はどれくらい小さいか How small is the smallest value in k random values from uniform distribution?
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N<-1000 M<-1000 Xs<-matrix(runif(N*M),N,M) Mins<-apply(Xs,1,min) plot(density(Mins)) abline(v=mean(Mins))
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このグラフをどう読む How do you read this graph?
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plot(sort(Mins)) abline(h=mean(Mins))
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同じデータからの２つのグラフ Two graphs from one data
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マルチプルテスティング Multiple testing
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Bonferroni’s method Sidak’s family-wise error rate
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ペアワイズ Pair-wise L(A,B) N*(N-1)/2 2つのものA,Bの間に定められる量
A value is defined between two items, A and B N*(N-1)/2
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ペアワイズでない比較 Non-pairwise comparison
３要素の比較 Three items to be compared ABC 0 0 0 N1 0 0 1 N2 0 1 0 N3 0 1 1 N4 1 0 0 N5 1 0 1 N6 1 1 0 N7 1 1 1 N8 AB 0 0 N1+N2 0 1 N3+N4 1 0 N5+N6 1 1 N7+N8 BC 0 0 N1+N5 0 1 N2+N6 1 0 N3+N7 1 1 N4+N8 CA 0 0 N1+N3 0 1 N2+N4 1 0 N5+N7 1 1 N6+N8
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ペアワイズでない比較 Non-pairwise comparison
３要素の比較 Three items to be compared ABC 0 0 0 0.125 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 ABC 0 0 0 0.25 0 0 1 0 1 0 0 1 1 0. 25 1 0 0 1 0 1 1 1 0 1 1 1 AB 0 0 0.25 0 1 1 0 1 1 BC 0 0 0.25 0 1 1 0 1 1 CA 0 0 0.25 0 1 1 0 1 1
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関係はいくつある How many “RELATIONS”?
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対立仮説が正しいとき When alternative hypothesis is true
非心カイ自乗分布 Non-central chi-square distribution 1 additional parameter
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強弱いろいろな対立仮説が成り立つとき When alternative hypotheses with various strength are true
No. parameter is 1.
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たくさんの仮説が正しいとき When many alternative hypotheses are true
False Discovery Rate
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