09基礎分析講習会
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- こおが いさし
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1 データ解析の意味を理解しないでパソコンで計算して 序論 誤差解析 何のために も意味がない 以下の本でちゃんと勉強しよう R. A. Millikan ミリカン 水滴の蒸発 大学院生H. Fletcher 水滴を油滴に 博士論文単名 140の観測のうち49個除外 データ削除 実験データを正しく扱うために 化学同人編集部編 油滴実験 Regener がもともとThompsonの実験室(Cambridge Univ.)でお こなっていた F. Ehrenhaft 副電荷 との 論争 勝利 １９２３年ノーベル物理学賞メンデル できすぎていた実 験 助手の庭師がメンデルの理論に合わせるようにカウ ントしたのかもしれない 科学の罠 過失と不正の科学史 アレクサンダー コーン 著 酒井シヅ 三浦雅弘訳 工作舎 /20 第1版第1刷発行: 2010/3/1 第4刷 加筆改訂を含む 前田 山本 加納著 1 身近なことかも 2 有効数字 こんな時君ならどうする 明日の朝までにデータを出すように言われた 物理的に不可能な状況 Positiveなデータが出ない場合 今後の に多大な 影響がある 忙しい指導教員は 途中の過程をほとんど見ず 結果 だけを重要視する 実験については 自分以外に詳しいものがいない データでおかしな点がある 捨てるべきか否か 再現性がない Best dataのみを採用すべきか否か 統計的な処理をすべきではないのか 3 4
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5 t t t-1(z%) t-1(z%) t-1(z%), z%: % 90% 95% 99%
6 x (x 1 x) 2 (x 2 x) 2 (x 5 x) 2 5 (x i x) 2 i=1 u t 1 (90%) u u 2 = i=1 (x i x) 2 1 ± t 1(90%)u u ± σ 23 24
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11 41 length / m time / s length / m time / s 43 44
12 45 length / m time / s 46 fxabx fxa bx
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14 x ± δx, y ± δy q = q(x, y) =x + y x = 10 ± 2g y = 20 ± 3g q = x + y = 30 g 2 q δq = (δx) x 2 + = = g 2 q (δy) y cm155cm cm 55 56
15 0.8 分布 身長 和の分布 トーテムポール 0.8 低 高 分布 0.6 低 0.4 高 0.2 小針アキ宏 確率 統計入門 岩波書店 身長 59 60
16 q = x y 2 q δq = (δx) x q (δy) y 2 = (δx) 2 +(δy) x ± δx, y ± δy,... q = q(x, y,...) 63 64
17 65 Fig log10 Fig. Harris, Quantitative Chemical Analysis c,! log10 I I0 Transmission: T 透過度 Absorbance: A 吸光度 I I0 = T A 実測しているのは T であり c,! Transmission: Absorbance: Aはその桁であると考えてよい これでいいのか = cl I I0 log10 T A T T*100 / % cl I I0 log10 T 測定誤差T ± "T が Aやcの見積もりに どのように きいてくるのか アレニウスプロット ph など多くの例がある 67 68
18 δc δt F = dc/c dt dc = da c A = dt T ln T log 10 (! " / " ) A!" A A!A T!T 69 70! l Ac 71 72
19 73 74 T ± δt A ± δa log 10 T A log 10 (T ± δt ) = log 10 T (1 ± δt T )= log 10 T log 10 (1 ± δt T ) = A ± δa ±δa = log 10 (1 ± δt T )= (log 10 e) ln(1 ± δt T ) (1) if δt/t << 1 δa = (log 10 e) δt T 75 (2) if δt T δa = (log 10 e) ln 2 +δa = (log 10 e) ln 0 + x = e y log 10 x = y log 10 e ln x = y ln e = y log 10 x = ln x log 10 e 76
20 c / M T ±δt c / M T ±δt c / M A ± A
21 wi fx xi = w i i x = i w ix i = σ 2 = = i w i i w ix i i w i(x i x) 2 i w ix 2 i x 2 1 = x = σ 2 = = x dxf(x) dxxf(x) dx(x x) 2 f(x) dxx 2 f(x) x random walk random walk 83 84
22 random walk random walk random walk p q (= 1-p) B,p (r) = r=0 C r p r q r =(p + q) =1 r=0 r rrr B,p (r) =! = 15! : rr! r!( r)! pr q r = C r p r q r 87 r r r = rb,p (r) = C r p r q r r = p r=0 r=0 σr 2 = r r 2 = r 2 r 2 = pq (p + q) = C r p r q r r=0 p d dp (p + q) = p(p + q) 1 = C r rp r q r r=0 p d dp p(p + q) 1 = p + ( 1)p 2 = C r r 2 p r q r r=0 88
23 Probability - 2r 2r =( 2r) = (1 2p) =0 (p =1/2) ( 2r) ( 2r) 2 = ( 2r) 2 ( 2r) 2 =[ 2 4r +4r 2 2 (1 2p) 2 ] 2 =[ p + 4(pq + 2 p 2 ) 2 (1 4p +4p 2 )] 2 =4pq 2 = 2 (p =1/2) lim + 1) t = r/ (Law of large numbers) 2) r : p = λ = const (Poisson distribution) 3) t = r r (Gauss distribution) σ r lim + t = r/ law of large numbers P (t) = dr dt B,p(r) =B,p (t) r = r = p r r 2 = r2 2 r2 2 p + ( 1)p2 = 2 2 p 2 2 = pq lim + F ( t ) t = r r σ r = r p pq F (t) = dr dt B,p(r) = pqb,p (r) G 0,1 (t) t t lim F (t) = G 0,1 (t) + G µ,σ (x) 1 2πσ exp[ (x µ) 2 /(2σ 2 )] 91 92
24 G µ,σ = 1 e (x µ)2 2σ 2 2πσ lim + p = λ = const. B,p P λ (r) = λr e λ r! p = 1 r 93 94!t t = t The probability that an event occurs in!t is equal to "!t, where " is the rate of the event. The probability that the events occur r times between t = 0 and t = t is given by binomial distribution P λ (r) = =! r!( r)! (λ t)r (1 λ t) r r! λ t 1 λ t r r!( r)! = (λt)r r! = (λt)r r! = (λt)r e λt r! ( 1)...( r + 1) r (1 λt/) r (1 λt/) (/λt)( λt) 1(1 1 )(1 2 )...(1 r 1 ) (1 λt/) r [(1 λt ) λt ] λt 1 1 e Poisson distribution 95 u t 96
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2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
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医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
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II 14 14-7-8 8/4 II (http://www.damp.tottori-u.ac.jp/~ooshida/edu/fluid/) [ (3.4)] Navier Stokes [ 6/ ] Navier Stokes 3 [ ] Reynolds [ (4.6), (45.8)] [ p.186] Navier Stokes I 1 balance law t (ρv i )+ j
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講義のーと : データ解析のための統計モデリング. 第２回
Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20
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ＪＭＰ V4 による生存時間分析
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確率論と統計学の資料
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4 Maxwell- Boltzmann N 1 4.1 T R R 5 R (Heat Reservor) S E R 20 E 4.2 E E R E t = E + E R E R Ω R (E R ) S R (E R ) Ω R (E R ) = exp[s R (E R )/k] E, E E, E E t E E t E exps R (E t E) exp S R (E t E )