# mloglik1a: Minus loglikelihood of an IHSEP model In IHSEP: Inhomogeneous Self-Exciting Process

 mloglik1a 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 for event times `jtms` on interval [0,TT].

### Usage

```mloglik1a(jtms, TT = max(jtms), nu, g,
Ig = function(x) sapply(x, function(y) integrate(g, 0, y)\$value),
tol.abs = 1e-12, tol.rel = 1e-12, limit = 1000
)

```

### 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`. `nu` A (vectorized) function. The baseline intensity function. `g` A (vectorized) function. The excitation function. `Ig` A (vectorized) function. Its value at `t` gives the integral of the excitation function from 0 to `t`. `tol.abs` A small positive number. The tolerance of the absolute error in the numerical integral of ν. `tol.rel` A small positive number. The tolerance of the relative error in the numerical integral of ν. `limit` An (large) positive integer. The maximum number of subintervals allowed in the adaptive quadrature method to find the numerical integral of ν.

### Details

This version of the mloglik function uses external C code to speedup the calculations. Otherwise it is the same as the `mloglik0` function.

### Value

The value of the negative log-liklihood.

### Author(s)

Feng Chen <feng.chen@unsw.edu.au>

`mloglik0`

### 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
mloglik1a(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){
mloglik1a(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)
```

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