# R/ModelU1.R In mfrdixon/MLEMVD: Maximum Likelihood Estimation for Diffusion Equations

#### Documented in ModelU1

```#' Compute the maximum likelihood estimate of Model U1
#'
#'
#' @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
#' ModelU1(0.4,0.3,0.1,c(0.1,0.2,0.3))
#'
ModelU1 <- function(x,x0,del,param,args=NULL){
a <- param[1]
b <- param[2]
sigma <- param[3]

y <- 2/(sqrt(x)*sigma)
y0 <- 2/(sqrt(x0)*sigma)
sx <- sigma*x^(3/2)
output <- list()
output\$llk <- -log(2*pi*del)/2 - log(sx)
+ (-(1/2))*(y - y0)^2 / del
+ (a*(-y^2 + y0^2)* sigma^2 + (-8*b + 6* sigma^2)*log(y/y0))/(4* sigma^2)
+ ( -((1/(24*y*y0* sigma^4))* (48*b^2 + 24*b*(-2 + a*y*y0)* sigma^2 + (9 - 24*a*y*y0 + a^2*y*y0*(y^2 + y*y0 + y0^2))* sigma^4)) )*del
+ ( -((48*b^2 - 48*b* sigma^2 + (9 + a^2*y^2*y0^2)* sigma^4)/ (24*y^2*y0^2* sigma^4)) )*(del^2/2)

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