Four lines below Equation (7), page 682, it must correctly read:
$Q=−12Hf(x)=−12∇∇Tf(x)$
In Equation (27), page 685, the logarithms are missing, it must correctly read:
$Iij(θ)=∫∂lnp(x|θ)∂θi∂lnp(x|θ)∂θjp(x|θ)dNx=-∫∂2lnp(x|θ)∂θi∂θjp(x|θ)dNx$
(27)
On page 687, below Equation (36), the derivations leading to Equation (40) must be corrected1 (the final result in Equation (41) does not change by this correction):
Treating the $C$-related part in (35) using $∂Cab∂Ccd=12δacδbd+δadδbc$ (here, symmetry of C must be taken into account) yields
$I(α1α2),(β1β2)=12∑k,l,m,nCkl-1∂Clm∂Cα1α2Cmn-1∂Cnk∂Cβ1β2=18∑k,l,m,nCkl-1(δlα1δmα2+δlα2δmα1)Cmn-1(δnβ1δkβ2+δnβ2δkβ1).$
(37)
Thus, one gets for the $C$-related part of $θ$ (taking the symmetry of $C-1$ into account)
$C:I(α1α2),(β1β2)=14Cα1β1-1Cα2β2-1+Cα1β2-1Cα2β1-1.$
(38)

The non-numbered equation below Equation (40), page 687, must be adopted accordingly:

The correctness of
$C:I(α1α2),(β1β2)-1=2Cα1β2Cβ1α2$
(40)
is proven directly by checking
$∑β1,β2I(α1α2),(β1β2)-1I(β1β2),(γ1γ2)=12δα1γ2δα2γ1+δα1γ1δα2γ2.$
On page 694, the derivation of Equation (83) must be corrected (again without consequences for the result in Equation (84)):
$∂σf∂Cmn=121σf∂∂Cmn∑i,j,k,l(ai-2x¯kQki)Cij(aj-2x¯lQlj)+2QijCjkQklCli=121σf∑i,j,k,l(ai-2x¯kQki)12(δimδjn+δinδjm)(aj-2x¯lQlj)12+Qij(δjmδkn+δjnδkm)QklCli+QijCjkQkl(δlmδin+δlnδim)=121σf∑k,l(am-2x¯kQkm)(an-2x¯lQln)+4QmkCklQln$
(83)

Note

1

The author is grateful to Zhenhua Li for pointing out this mistake to be corrected here.