mloglik0 | R Documentation |
Calculates the minus loglikelihood of an IHSEP model with given
baseline inensity function ν and excitation function g
for event times jtms
on interval [0,TT].
mloglik0(jtms, TT = max(jtms), nu, g, Ig=function(x)sapply(x,function(y)integrate(g,0,y)$value))
jtms |
A numeric vector, with values sorted in ascending order. Jump times to fit the inhomogeneous self-exciting point process model on. |
TT |
A scalar. The censoring time, or the terminal time for
observation. Should be (slightly) greater than the maximum of |
nu |
A (vectorized) function. The baseline intensity function. |
g |
A (vectorized) function. The excitation function. |
Ig |
A (vectorized) function. Its value at |
The value of the negative log-liklihood.
Feng Chen <feng.chen@unsw.edu.au>
## simulated data of an IHSEP on [0,1] with baseline intensity function ## nu(t)=200*(2+cos(2*pi*t)) and excitation function ## g(t)=8*exp(-16*t) data(asep) ## get the birth times of all generations and sort in ascending order tms <- sort(unlist(asep)) ## calculate the minus loglikelihood of an SEPP with the true parameters mloglik0(tms,TT=1,nu=function(x)200*(2+cos(2*pi*x)), g=function(x)8*exp(-16*x),Ig=function(x)8/16*(1-exp(-16*x))) ## calculate the MLE for the parameter assuming known parametric forms ## of the baseline intensity and excitation functions ## Not run: system.time(est <- optim(c(400,200,2*pi,8,16), function(p){ mloglik0(jtms=tms,TT=1, nu=function(x)p[1]+p[2]*cos(p[3]*x), g=function(x)p[4]*exp(-p[5]*x), Ig=function(x)p[4]/p[5]*(1-exp(-p[5]*x))) }, hessian=TRUE,control=list(maxit=5000,trace=TRUE)) ) ## point estimate by MLE est$par ## standard error estimates: diag(solve(est$hessian))^0.5 ## End(Not run)
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