Kalman-filter log-likelihood of counts observed at times
Delta, 2 Delta, ..., n Delta under the Gaussian (linear noise)
approximation of the density-dependent Markov jump process defined by
model. Over each interval the ordinary differential equation of the
mean, its resolvent and the Lyapunov equation of the state-noise
covariance are integrated jointly by the classical Runge-Kutta method in
compiled code. Incidence observations are handled with event counters
and an augmented state that contains the state at the start and the end
of each interval.
Usage
ga_loglik(
model,
theta,
init,
data,
obs,
N,
Delta = 1,
nsub = 10L,
varying = NULL,
full = FALSE
)Arguments
- model
A
ga_model().- theta
Named list or vector with the rate parameters of
modeland any parameters named inobs.- init
Named vector of initial fractions, one per compartment (normalised to sum to one).
- data
Matrix or data frame of counts, one column per element of
obs(in the same order), one row per interval.NAmarks a missing count.- obs
List of
ga_incidence()/ga_prevalence()streams.- N
Population size.
- Delta
Length of the observation interval.
- nsub
Runge-Kutta steps per interval.
- varying
Optional named list of time-varying rate parameters: each element is a vector with one value per interval, overriding the constant value in
theta.- full
If
TRUE, return the list with one-step-ahead predicted means (fitted) and standard deviations (sd) of the counts and the path of the mean (x, fractions) instead of the scalar.