To estimate the error in the best-fitting parameter values that we find, we assume P u | x_i, f_i, σ_i
n_u
u^0
L(u)
u^0
Zero at
u^0
+
∑_i=0^n_u-1 ∑_j=0^n_u-1 _u^0 + O u - u^0^3
Since the logarithm of a Gaussian distribution is a parabola, the quadratic terms in the above expansion encode the Gaussian component of the probability distribution P u | x_i, f_i, σ_i
u^0
Q
^T
u^0
A
L
n_u
u_0 ... u_n_u-1
e_i
A
λ_i
1/σ_i^2
σ_i
A
L
k
A_ii
-1/σ_i^2
u_i
Footnotes