# mloglik1e: Minus loglikelihood of an IHSEP model In IHSEP: Inhomogeneous Self-Exciting Process

 mloglik1e R Documentation

## Minus loglikelihood of an IHSEP model

### Description

Calculates the minus loglikelihood of an IHSEP model with given baseline inensity function ν and excitation function g(x)=∑ a_i exp(-b_i x) for event times `jtms` on interval `[0,TT]`.

### Usage

```mloglik1e(jtms, TT, nuvs, gcoef, InuT)
```

### 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 `jtms`. `nuvs` A numeric vector, giving the values of the baseline intensity function ν at the jumptimes `jtms`. `gcoef` A numeric vector (of 2k elements), giving the parameters `(a_1,...,a_k,b_1,...,b_k)` of the exponential excitation function g(x)=∑_{i=1}^k a_i*exp(-b_i*x). `InuT` A numeric value (scalar) giving the integral of ν on the interval `[0,TT]`.

### 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>

`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
mloglik1e(tms,TT=1,nuvs=200*(2+cos(2*pi*tms)),
gcoef=8*1:2,
InuT=integrate(function(x)200*(2+cos(2*pi*x)),0,1)\$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){
mloglik1e(jtms=tms,TT=1,
nuvs=p[1]+p[2]*cos(p[3]*tms),
gcoef=p[-(1:3)],
InuT=integrate(function(x)p[1]+p[2]*cos(p[3]*x),
0,1)\$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)
```

IHSEP documentation built on Sept. 17, 2022, 1:05 a.m.