182 Modeling and Inverse Problems in the Presence of Uncertainty
assumptions on the error process could lead to the more dir ect estimation
of the underlying probability measure itself. This is the goal of the non-
parametric maximum likelihood (NPML) method proposed by Mallet [52].
This approach assumes that some level of longitudinal data is available for
each individual. Indeed, one assumes the population under study consists o f
i individuals, 1 ≤ i ≤ N
T
, and that for each individual i, there is longitudinal
data {y
ij
}, j = 1, 2, . . . , N
i
, available for the ith individual. The dyna mics
for the ith individual a re assumed to be described by the mathematical model
˙x
i
(t) = g
i
(t, x
i
(t); θ
i
, ψ). (5.39)
In order to simplify notation we assume here ...