EM1partial: Partial EM algorithm for the RHawkes process, version 1

In RHawkes: Renewal Hawkes Process

Partial EM algorithm for the RHawkes process, version 1

Description

Calculates the RHawkes model parameters via a partial Expectation-Maximization (EM1) algorithm of Wheatley, Filimonov and Sornette (2016).

Usage

EM1partial(tms, cens, pars, maxiter = 1000, tol = 1e-8,
         h.fn = function(x, p) dexp(x, rate = 1 / p),
         mu.fn = function(x, p){
              exp(dweibull(x, shape = p[1], scale = p[2], log = TRUE) -
              pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, log.p = TRUE))
         },
         H.fn = function(x, p) pexp(x, rate = 1 / p),
         logg.fn = function(x, p){
              dweibull(x, shape = p[1], scale = p[2], log = TRUE) -
              pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, log.p = TRUE) 
              - (x / p[2])^p[1]},
         Mu.fn = function(x, p){
              - pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, log.p = TRUE)
         })

Arguments

tms	A numeric vector, with values sorted in ascending order. Event times to fit the RHawkes point process model.
cens	A scalar. The censoring time.
pars	A numeric vector containing the parameters of the model, in order of the immigration parameters μ(.), offspring parameters h(.) and lastly the branching ratio η(.).
maxiter	The maximum number of iterations to perform.
tol	The algorithm stops when the difference between the previous iteration and current iteration parameters sum is less than tol.
h.fn	A (vectorized) function. The offspring density function.
mu.fn	A (vectorized) function. The immigration hazard function.
H.fn	A (vectorized) function. Its value at t gives the integral of the offspring density function from 0 to t.
Mu.fn	A (vectorized) function. Its value at t gives the integral of the immigrant hazard function from 0 to t.
logg.fn	A (vectorized) function. The log of the immigrant distribution function.

Value

iterations	The number of iterations until convergence
diff	The absolute sum of the difference between the final two parameter estimates
pars	The parameter estimates from the EM algorithm

Author(s)

Feng Chen <[e-mail]> Tom Stindl <[e-mail]>

Examples

## Not run: 
## simulated data
tms <- sort(runif(100,0,100))
## the slower version of the EM algorithms on simulated data with default 
## immigrant hazard function
## and offspring density
system.time( est1 <- EM1partial(tms, 101, c(2,1,0.5,1)) )

## End(Not run)

RHawkes documentation built on May 5, 2022, 5:06 p.m.