Laplace Approximation

In ctsmTMB: Continuous Time Stochastic Modelling using Template Model Builder

The likelihood function is the joint density of the observations i.e.

$$ L(\theta) = f(Y) $$ Now consider instead the joint density of both states $X$ and observations $Y$. This can be written as

$$ f(Y) = \int_{X} f(X,Y) \, \mathrm{d}X = \int_{X} \exp \log f(X,Y) \, \mathrm{d}X $$

ctsmTMB documentation built on April 12, 2025, 1:45 a.m.