# R/ModelU2.R In mfrdixon/MLEMVD: Maximum Likelihood Estimation for Diffusion Equations

#### Documented in ModelU2

```#' Compute the maximum likelihood estimate of Model U2
#'
#'
#' @param x Observation of the state variable at time t
#' @param x0 Observation of the state variable at time t-1
#' @param del The time step between the current and previous observation
#' @param param The parameter 3-vector
#' @param args Not currently used
#' @export output a list with a llk variable storing the result of the log likelihood calculation
#' @examples
#' ModelU2(0.4,0.3,0.1,c(0.1,0.2,0.3))
#'
ModelU2 <- function(x,x0,del,param,args=NULL)
{
if (length(param)==3){
a <- param[1]
b <- param[2]
d <- param[3]
}
else if (length(param)==2){
a <- 0
b <- param[1]
d <- param[2]
}
y <- log(x)/d
y0 <- log(x0)/d

E <- exp(1)
sx <- d*x

cYm1 <- (-(1/2))*(y - y0)^2
cY0 <- (E^((-d)*y) - E^((-d)*y0))*(-(a/d^2)) + (y - y0)*(b/d - d/2)

if (y != y0)
{
cY1 <- (a^2/(4*d^3))*((E^(-2*d*y) - E^(-2*d*y0))/(y - y0)) + ((a*b)/d^3 - a/d)*((E^((-d)*y) - E^((-d)*y0))/(y - y0)) -  (2*b - d^2)^2/(8*d^2)
cY2 <- (-(a^2/(2*d^3)))*((E^(-2*d*y) - E^(-2*d*y0))/(y - y0)^3) +
((2*a)/d - (2*a*b)/d^3)*((E^((-d)*y) - E^((-d)*y0))/(y - y0)^3) + (-(a^2/(2*d^2)))*((E^(-2*d*y) + E^(-2*d*y0))/(y - y0)^2) +
(a - (a*b)/d^2)*((E^((-d)*y) + E^((-d)*y0))/(y - y0)^2)
}
else
{
cY1 <- (-4*a^2 - 8*a*(b - d^2)*E^(d*y) - (-2*b + d^2)^2*E^(2*d*y))/(E^(2*d*y)*(8*d^2))
cY2 <- ((1/6)*a*(-2*a + (-b + d^2)*E^(d*y)))/E^(2*d*y)
}

output <- list()
output\$llk <- (-(1/2))*log(2*pi*del) - log(sx) + cYm1/del + cY0 +  cY1*del + cY2*(del^2/2)

return(output)
}
```
mfrdixon/MLEMVD documentation built on May 1, 2018, 11:38 p.m.