mloglik1c {IHSEP} | R Documentation |
Minus loglikelihood of an IHSEP model
Description
Calculates the minus loglikelihood of an IHSEP model with given
baseline inensity function \nu
and excitation function g(x)=a
exp(-b x)
for event times jtms
on interval [0,TT]
.
Usage
mloglik1c(jtms, TT, nu, gcoef, Inu)
Arguments
jtms |
A numeric vector, with values sorted in ascending order. Jump times to fit the inhomogeneous self-exciting point process model on. |
TT |
A scalar. The censoring time, or the terminal time for
observation. Should be (slightly) greater than the maximum of |
nu |
A (vectorized) function. The baseline intensity function. |
gcoef |
A numeric vector (of two elements), giving the parameters (a,b) of the exponential excitation function g(x)=a*exp(-b*x). |
Inu |
A (vectorized) function. Its value at |
Details
This version of the mloglik function uses external C code to speedup
the calculations. When given the analytical form of Inu
or a
quickly calculatable Inu
, it should be (substantially)
faster than mloglik1a
when calculating the (minus log)
likelihood when the excitation function is exponential. Otherwise it
is the same as mloglik0
, mloglik1a
, mloglik1b
.
Value
The value of the negative log-liklihood.
Author(s)
Feng Chen <feng.chen@unsw.edu.au>
See Also
mloglik0
, mloglik1a
and mloglik1b
Examples
## simulated data of an IHSEP on [0,1] with baseline intensity function
## nu(t)=200*(2+cos(2*pi*t)) and excitation function
## g(t)=8*exp(-16*t)
data(asep)
## get the birth times of all generations and sort in ascending order
tms <- sort(unlist(asep))
## calculate the minus loglikelihood of an SEPP with the true parameters
mloglik1c(tms,TT=1,nu=function(x)200*(2+cos(2*pi*x)),
gcoef=8*1:2,
Inu=function(y)integrate(function(x)200*(2+cos(2*pi*x)),0,y)$value)
## calculate the MLE for the parameter assuming known parametric forms
## of the baseline intensity and excitation functions
## Not run:
system.time(est <- optim(c(400,200,2*pi,8,16),
function(p){
mloglik1c(jtms=tms,TT=1,
nu=function(x)p[1]+p[2]*cos(p[3]*x),
gcoef=p[-(1:3)],
Inu=function(y){
integrate(function(x)p[1]+p[2]*cos(p[3]*x),
0,y)$value
})
},hessian=TRUE,control=list(maxit=5000,trace=TRUE))
)
## point estimate by MLE
est$par
## standard error estimates:
diag(solve(est$hessian))^0.5
## End(Not run)