UZHjpfister/papers/Pfister_02.pdf · 2015. 9. 24. · \ x tatax 1h4:x, 8 lw q* 9t (4 'v 7*1s4 'x...
Transcript of UZHjpfister/papers/Pfister_02.pdf · 2015. 9. 24. · \ x tatax 1h4:x, 8 lw q* 9t (4 'v 7*1s4 'x...
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exp
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i=1
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2
n∑
i=1
µ2i
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= exp
[n∑
i=1
µiZi −1
2
n∑
i=1
µ2i
](2π)−n/2 exp
[−1
2
n∑
i=1
z2i
]dz1 . . . dzn
= (2π)−n/2 exp
[−1
2
n∑
i=1
(zi − µi)2]
dz1 . . . dznR `NLA]La�Z
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Lλo (xo) =
∫
Ωh
Lλ(xo,xh)dRh
dSλ,xoh(xh)dS
λ,xoh (xh)
=
∫
Ωh
exp{ 1
σ2
∫ T
0
µo(x(t),λ) · dxo(t)
− 12σ2
∫ T
0
‖µo(x(t),λ)‖2dt}
dSλ,xoh (xh)R `NLA] � Z
Y�* (-, UKI-I , * u V7B X , TAU.�VAW[4 , V2e ( 4:V2*51Sλ,xoh
9�VAT W (Nz 4i.�Xn358�1^8 , X ,M\= ( X�TAX
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∂ log Lλ(x)
∂Wij=
1
σ2
∫ T
0
∂µ(x(t),λ)
∂Wij(dx(t)− µ(x(t),λ)dt)
=1
σ2
(bji(x)−
N∑
n=1
Wjnain(x)
) R `NL `9`5ZU/9XR\
bij(x) =
∫ T
0
ϕ(xi(t))dxj (t) +1
τj
∫ T
0
ϕ(xi(t))xj(t)dtR `-L `9a�Z
aij(x) =
∫ T
0
ϕ(xi(t))ϕ(xj (t))dtR `-L ` �HZ
X+4
∂ log Lλ(x)
∂γi=
1
σ2
∫ T
0
∂µ(x(t),λ)
∂γi(dx(t)− µ(x(t),λ)dt)
=1
σ2
−γi
∫ T
0
xi(t)2dt +
N∑
j=1
∫ T
0
ϕ(xj(t))Wjixi(t)dt
−∫ T
0
xi(t)dxi(t)
) R `NL ` � Z
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∇λ log L̂λo (xso) =M∑
m=1
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