第二版勘误表；.pdf

1  Æ (2022.05) (*fi4= 4 4 (d,)      B http://stuff.ustc.edu.cn/ lwei/books.htm P , 4 1 R~ v http://staff.ustc.edu.cn/∼lwei/books.htm    !i stuff ~1 u G: a ii ∼ B http://stuff.ustc.edu.cn/ zwp/books/bayes/bayes.htm P , 4 1 R~ v http://staff.ustc.edu.cn/∼zwp/books/Bayes/bayes.htm    !i stuff ~1 u G: a, i bayes/ ~14℄K     ii ∼  | -1 RR~ B n5 () V (classical school) j \.Vma#v1t v n5 () V (classical school) j \.Vma#v1t P2 , -2  4 8 R~ B θ ∈ Θ, R(θ, δ (x)) 6 R(θ, δ (x)), v θ ∈ Θ, R(θ, δ ) 6 R(θ, δ ),     !i~ δ (x) G: δ , δ (x) G: δ , L 1 & P12 ,      1 2 1 2 1 1 2 2 4 9 R~ B R;℄ θ ∈ Θ, R(θ, δ (x)) ≡ R(θ, δ (x)), v R;℄ θ ∈ Θ, R(θ, δ ) ≡ R(θ, δ ),     !i~ δ (x) G: δ , δ (x) G: δ , L 1 & P12 ,      1 2 1 1 1 2 2 2 4 11 R~ B R(θ, δ (x)) 6 R(θ, δ(x)), v R(θ, δ ) 6 R(θ, δ),     !i~ δ (x) G: δ , δ(x) G: δ, L 1 & P12 ,      ∗ ∗ ∗ ∗ b G:+P B 2 4 1 R~ B ! R(θ, δ(x)) :DHS+ v ! R(θ, δ) :DHS+     !i~ δ(x) G: δ, O 1 & P13 ,      4 3 R~ Z B R (δ(x)) = R(θ, δ(x))dF (θ) = E [R(θ, δ(X))] Z v R (δ) = R(θ, δ)dF (θ) = E [R(θ, δ)]        !i~ δ(x) G: δ, O 2 & iN' <&1 δ(X) G: δ, O 1 & P13 ,         π π π Θ π π π Θ 4 8 R~ B  R (δ (x)) 6 R (δ (x))  v  R (δ ) 6 R (δ )      !i~ δ (x) G: δ , δ (x) G: δ , L 1 & P13 ,      π 1 π 1 π π 2 2 1 1 2 2 4 10 R~ B R (δ (x)) 6 R (δ(x)), v R (δ ) 6 R (δ),     !i~ δ (x) G: δ , δ(x) G: δ, L 1 & P13 ,      π π ∗ ∗ π π ∗ ∗ R~ B T = T (X) )℄K9b~p T :"C9b~1"Y8h) v T = T (X) )℄K9b~p T :"C9b~1"Y8h)     !'& T )X6O 2 & P13 , -7      | -1 R~ B ! T = T (X) : θ 1"C9b~ S = ϕ(T) )℄℄;e1[p S = ϕ(T) Z) v ! T = T (X) : θ 1"C9b~ S = ϕ(T ) )℄℄;e1[p S = ϕ(T ) Z)     !'& T )X6O 3 & P13 , -2      P15 , 4 5 R (' (1.4.3)) ~ 3              B f (x, ϕ) = C (ϕ) exp ∗  n P i=1  k P  ϕi Ti (x) h(x),  ϕi Ti (x) h(x), v f (x, ϕ) = C (ϕ) exp !iUT J n G: k ∗ i=1 4 13 R~ B 3. g(θ) = θ $' (1.4.8) :  v ' (1.4.8) !: C-R 2'3. g(θ) = θ $' (1.4.8) : P19 ,   P26 ,          4 2 R~ n o B f (x) = C(θ) exp P θ T (x) h(x), k θ j j j=1 P v f (x) = C(θ) exp θ T (x) h(x),         !i θ G:X6O 2 & P26 ,                      n k θ j j j=1 o 4 4-5 R~ B E (T (x)) = − ∂ ln C(θ) 1 ∂C(θ) = − C(θ) ∂θj ∂θj , ∂ 2 ln C(θ) Cov(Tj (x), Ts (x)) = − ∂θj ∂θs . θ j v E (T (x)) = − ∂ ln C(θ) 1 ∂C(θ) = − C(θ) ∂θj ∂θj , ∂ 2 ln C(θ) Cov(Tj (x), Ts (x)) = − ∂θj ∂θs . θ j !i θ G:X6O 5 & 4 7 R (C5 2 5 12 (3)) ~ B g:: n, =}+: µ, t:+: σ 1℄l t C : T (n, µ, σ ) (n Q8).   v g:: n, =}+: µ, t:+: σ 1℄l t C : T (n, µ, σ ) (n Q8σ ^x ); P66 ,    1 1  4 9 R~ B ! X : p ;0^M~ X ∼ N (θ, σ I), ~ σ > 0 ^x
  v ! X : p ;0^M~ X ∼ N (θ, σ I).
P87 ,    p p 2 2 2 2 2 2 4 4 10 R~ B pM8 θ $X1|WH :S+:   v pM8 θ U σ $X1|WH :S+: P87 ,    2 4 11 R~ B f (x , · · · , x | θ)   v f (x , · · · , x | θ, σ ) P87 ,    1 n 1 n 2 4 6 R~ B βe = X X + kI
X X β̂ + kµ
= Σe X X β̂ + kµ



e X X β̂ + kµ βe = X X + kI X X β̂ + kµ = Σ v    !G I : I P99 ,     −1 τ −1 τ p τ τ τ τ p  4 3 R~ B hZWCZs)ZWC%> n5A?   v hZWCZs)ZWC%>w/in5A? P107 ,    4 8 R~ B nfKS\0m/z χ v nfKS\0m/z χ     !i 10.612 G: 10.621 P120 ,      P120 ,                  2 5.9828 (0.10) = 10.612. 2 5.9828 (0.10) = 10.621. 4 10 R~ + 59742) B θ̂ = 2(tχ +(η)β) = 2(40000 = 18798 (N$). 10.612 L 2 f + 59742) v θ̂ = 2(tχ +(η)β) = 2(40000 = 18782 (N$). 10.621 !i 10.612 G: 10.621, i 18798 G: 18782 L 2 f 5 4 10-11 R~ B π(c |t) = π(122007|t) = 0.000000998 , k . E  % θ 1sQ-: 0.90 1 HPD sQe v π(c |t) = π(122007|t) = 0.000000998 , k .   G'&h k > k .      E  % θ 1sQ-: 0.90 1 HPD sQe     !7 ℄R P , 4 19-20 R~   B (c)  p − 0.9 < 0, pi k FzM k ,  (1) U (2).       R ,E        (c)  p − 0.9 < 0, pi k FzM k ,  (1) U (2).  v ! 4.3.2 ;&%:=$3' k > k . 1+:=$3' k , k /A      5- k > k , <24 (b) , (c) ? k ')>."98*#6('07       HPD sQe1 R ,E     !7  ! 4.3.2 P122 ,             1 2 2 2 2 2 122 1 1 1 2 2 1 2 1 | -5 R~ B π(d |x) = π(6.149878|x) = 0.05190256 , k . E  % θ 1sQ-: 0.95 1 HPD sQe π(d |x) = π(6.149878|x) = 0.05190256 , k . v   G'&h k > k .      E  % θ 1sQ-: 0.95 1 HPD sQe     !7 ℄R P , 4 4-5 R~   B (c)  p − 0.95 < 0, pi k FzM k ,  (1) U (2).       R ,E    v (c)  p − 0.95 < 0, pi k FzM k ,  (1) U (2).      syTY3{%1)g
4.3.2 4%1?5'&U 
`      HPD sQe1 R ,E P123 , -6             1 2 2 2 2 2 124 1 1 4 6 R~ B FWCp  v FWCp θ 1ZWC: P , 4 10 R~ P125 ,   125 6 B o*.8hEsw . n "C+$ π (θ|x) m/E) N µ (x), V (x)
,  v o*.8hEsw . n "C+$ θ 1ZWC π (θ|x) m/E) N µ (x), V (x)
, P , 4 1 R~   B ! 4.3.2 J 4.3.1 4=R~1 5 KC=+g{ 4.3.5 ~1 R ,M%  v ! 4.3.3 J 4.3.1 4=R~1 5 KC=+g{ 4.3.5 ~1 R ,M% P , -2 R~  1  B B = αα ππ = αα = 8.43 .      α π α 1 = = . v B (x) =   α π α 8.43     ! B (x) ~ x :BX6 P , -6 | -5 R~   B H : θ = θ ↔ H : θ 6= θ .      s)n59b~ g1℄wfW?5      H : θ = θ ↔ H : θ 6= θ , (4.4.6) v   ℄      π n π π n 126 130 π 0 1 0 1 0 1 π 0 1 0 1 0 1 π 133       0 0 1 0 0 0 1 0 H0′ : θ = θ0 ↔ H1′ : θ > θ0 (θ < θ0 ). (4.4.7) fW?5 (4.4.6) )n59b~ g1℄wfW?5 P , 4 2 R~  B E r H : θ = θ ↔ H : θ 6= θ 1 \.fWV/%    v fW?5 (4.4.7) 1A?jfW?5 (4.4.6) 1A?w/E r    fW?5 (4.4.6) 1 \.fWV/% P -P [~2hN'1TLeq 2 v> f1N'TZLe6u
P , -3 | -2 R~  B : Z 1sQD+: 1 − α (0 < α < 1) 1ZWke v : Z 1sQ-: 1 − α (0 < α < 1) 1ZWke P , 4 1 R~  B sg Z 1 1 − α 1ZWke: v sg Z 1sQ-: 1 − α 1ZWke: P , 4 14-15 R (C5 25 ) ~ 134 0 134 139 140 142 135 0 1 0 π 7  B s}Kd!1ZWH ZWHU \.b v s}Kd!1ZWH ZWHU \.b;fW?5%k .θ=θ π g (θ), . θ 6= θ P , -6 R (C5 30 ) ~ (   π , . θ = 1/2     v π(θ) = π g (θ), . θ 6= 1/2        142 B π(θ) = ( π0 , 1 0 1 0 0 1 1  4 7 R~ Z B R (δ) = E [R(θ, δ(x))] = R(θ, δ(x))π(θ)dθ Z v R (δ) = E [R(θ, δ)] = R(θ, δ)π(θ)dθ        !i~ δ(x) G: δ, O 2 & P146 ,         θ π Θ θ π Θ 4 10 R~ Z   B = R(δ(x)|x)m(x)dx = E R(δ(x)|x) , Z   v = R(δ(x)|x)m(x)dx = E R(δ(X)|X) ,        !i R(δ(x)|x) ~X6NP x G:X6+P P146 ,         X (5.2.3) X (5.2.3) X X X, O2& 4 11 R~ B ` R (δ(x)) = E R(θ, δ(x)) = E R(δ(x)|x), v ` R (δ) = E R(θ, δ) = E R(δ(X)|X),    !i R (δ(x)) G: R (δ), i R(θ, δ(x)) G: R(θ, δ), L 1 &     i R(δ(x)|x) ~X6NP x G:X6+P X, O 2 & P146 ,         θ π X θ π π X π 4 12 R~ B iDHS+ R(θ, δ(x)) θ 1FWC π(θ) qz v iDHS+ R(θ, δ) θ 1FWC π(θ) qz     !i~ δ(x) G: δ, O 1 & P146 ,      P146 , -4 R~ 8 Z         Z B R(δ(x)|x) = L(θ, δ(x))π(dθ|x) > L(θ, δ )π(dθ|x) = R(δ (x)|x) Z Z v R(δ(x)|x) = L(θ, δ(x))π(dθ|x) > L(θ, δ (x))π(dθ|x) = R(δ (x)|x)        !i~ L(θ, δ ) G: L(θ, δ (x)), O 1 & Θ π π Θ π Θ π Θ π π R~ P146 , -2 Z Z    Rπ (δ(x)) = R(δ(x) | x)m(x)dx > R(δπ (x)|x)m(x)dxx = Rπ (δπ (x)).    X X   Z Z Rπ (δ) = R(δ(x) | x)m(x)dx > R(δπ (x)|x)m(x)dxx = Rπ (δπ ).   X X      Rπ (δ(x)) Rπ (δ), Rπ (δπ (x)) Rπ (δπ ), 1 B v !i~ G: i~ G: L & 4 2 R (8x 5.3.3) ~ B op;1"S+S+ (absolute error loss function) L(θ, a) = |θ − a| E  v op;z1"S+S+ (absolute error loss function) L(θ, a) = |θ − a| E P150 ,   4 3 R~ Z Z B = (θ − 90)π(θ|x)dθ + 2 (θ − 90)π(θ|x)dθ P158 ,                110 Z ∞ 90 110 x, O 1 & x, O 1 & x, O 1 & 4 6 R~ Z Z B = (90 − θ)π(θ|x)dθ + (θ − 110)π(θ|x)dθ 90 −∞ Z 90 ∞ 110 Z ∞ v = (90 − θ)π(θ|x)dθ + (θ − 110)π(θ|x)dθ !iZ℄K_C~X6NP x G:BX6NP −∞ 110 4 9 R~ Z Z B = 2 (110 − θ)π(θ|x)dθ + P158 ,                  90 Z 110 ∞ v = (θ − 90)π(θ|x)dθ + 2 (θ − 90)π(θ|x)dθ !iZ℄K_C~X6NP x G:BX6NP P158 ,                  110 90 110 −∞ 90 Z 90 (110 − θ)π(θ|x)dθ Z 110 v = 2 (110 − θ)π(θ|x)dθ + (110 − θ)π(θ|x)dθ !iZ℄K_C~X6NP x G:BX6NP P159 , -11 −∞ | -10 R~ 90 9 B ! C(x) = (d (x), d (x))) : θ 1℄KePb v ! C(x) = [d (x), d (x))] : θ 1℄KePb     !iePb)muTG:AuT      1 2 1 2 | -6 R~ B sj ĝ : g(θ) 1 \.l<  v sj ĝ : g(θ) 1 \.l (Pb) < P161 , -7   ∗ ∗ 4 13 R~ B sj ĝ :FWC π (θ) yE1 \.l<  v sj ĝ :FWC π (θ) yE1 \.l (Pb) < P163 ,   k k k k R~ P166 , -3  R(θ, δ(X)) = E X|θ [δ(X) − θ]2     B v R(θ, δ) = E [δ(X) − θ]     !i~ R(θ, δ(X)) G: R(θ, δ), O 1 & X|θ 2 R~ P166 , -1      R(θ, δ(X)) = E X|θ (X − θ)2 + E X|θ δ02 (X) + 2E X|θ (X − θ) · E X|θ δ0 (X)         R(θ, δ) = E X|θ (X − θ)2 + E X|θ δ02 (X) + 2E X|θ (X − θ) · E X|θ δ0 (X)     R(θ, δ(X)) R(θ, δ), 1 B v !i~ G: O & 4 18 R~ B fw?*o δ (x), %0;℄ θ ∈ Θ, v fw?*o δ = δ (x), %0;℄ θ ∈ Θ,     !o δ (x) ~ x )X6 P168 ,      ∗ ∗ ∗ ∗ 4 2 R~ B :o61{! X ∼ N (θ, 1),  v  :o61{! X ∼ N (θ, 1), P174 ,   P184 , 4 8-9 R (C5A5 8) ~ 10                B (4(zfY2'      m N −m N +1 = , k = 0, 1, · · · , n) . k n−k n+1 m=1      N P m N −m N +1 = , k = 0, 1, · · · , n) . k n−k n+1 m=0 N P v (4(zfY2' !iUT~ m = 1 G: m = 0. 4R (C5A5 19) ~ B (1) w L(θ, d) > 0, v (1) w L(θ, d) > 0,     !i > 0 G: > 0. P185 ,       | R~ B G s}K_C9hG'l-)s_%fL+z_CA? ( IMSL ℄rI._CA?) vIO3 ms}K_C   v G s}K_C9hG'l-)L+z_CA? IMSL (International      Mathematics and Statistics Library) ℄rI._CA?s_ÆfvvIO3m     s}K_C P189 , -6 -4        (International Mathematics and Statistics Library)      4 1 R~ B  6.3.2 M%)$& θ̂ = 0.5 %>17,kR`201Pb θ̂ = 0.62682.   v  6.3.2 M%)$z θ̂ = 0.5 %>17,kR`201Pb θ̂ = 0.62682. P196 ,    (0) (0) 4 12-13 R~ B
X = (X , · · · , X ) : R ~10^~|WC f (x) :Æ#XC8 a d − 1 ;10^~ v
X = (X , · · · , X ) : R ~10^M~|WC f (x) :Æ#XC8     a d − 1 ;10^M~       !i~G:M~O}& P225 ,            1 d 1 d d d R~ B '$1ÆC: µ, σ 1ZWC  v ~ µ , σ , a U b j^x'$1ÆC: µ, σ 1ZWC P228 , -11   2 0 2 0 0 0 2 11  P333 , -3 R℄Rq E >I Rao C R. 1973. Linear Statistical Inference and Its Applications [M]. 2nd ed. New York: wiley.