mloglik1d | R Documentation |
Calculates the minus loglikelihood of an IHSEP model with given
baseline intensity function ν and excitation function
g(x)=∑ a_i exp(-b_i x) for event times jtms
on interval
[0,TT]
.
mloglik1d(jtms, TT, nu, gcoef, Inu)
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 2k elements), giving the parameters
|
Inu |
A (vectorized) function. Its value at |
This function calculates the minus loglikelihood of the inhomegeneous
Hawkes model with background intensity function ν(t) and
excitation kernel function g(t)=∑_{i=1}^{k} a_i e^{-b_i t}
relative to continuous observation of the process from time 0 to time
TT
. Like mloglik1c
, it takes advantage of the Markovian
property of the intensity process and uses external C++ code to speed
up the computation.
The value of the negative log-liklihood.
Feng Chen <feng.chen@unsw.edu.au>
mloglik1c
## 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 mloglik1d(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)$value) ## calculate the MLE for the parameter assuming known parametric forms ## of the baseline intensity and excitation functions ## Not run: system.time(est <- optim(c(400,200,2*pi,8,16), function(p){ mloglik1d(jtms=tms,TT=1, nu=function(x)p[1]+p[2]*cos(p[3]*x), gcoef=p[-(1:3)], Inu=function(y){ integrate(function(x)p[1]+p[2]*cos(p[3]*x), 0,y)$value }) },hessian=TRUE,control=list(maxit=5000,trace=TRUE), method="BFGS") ) ## point estimate by MLE est$par ## standard error estimates: diag(solve(est$hessian))^0.5 ## End(Not run)
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