timedelay (version 1.0.2)

entirelogprofilelikelihood: Calculating the entire profilel likelihood curve over the given grid values of the time delay

Description

entirelogprofilelikelihood calculates the entire profilel likelihood curve over the given grid values of the time delay.

Usage

entirelogprofilelikelihood(data, grid, initial, data.flux, delta.uniform.range, micro)

Arguments

data

The data set

grid

A vector containing values of the time delay on which the profile likelihood values are calculated. We recommend using the grid interval equal to 0.1.

initial

The initial values of the other model parameters (mu, log(sigma), log(tau), beta). We take log on sigma and tau for numerical stability.

data.flux

"True" if data are recorded on flux scale or "FALSE" if data are on magnitude scale.

delta.uniform.range

The range of the Uniform prior distribution for the time delay. The feasible entire support is c(min(simple[, 1]) - max(simple[, 1]), max(simple[, 1]) - min(simple[, 1])).

micro

It determines the order of a polynomial regression model that accounts for the difference between microlensing trends. Default is 3. When zero is assigned, the Bayesian model fits a curve-shifted model.

Value

The outcome of entirelogprofilelikelihood is the values of the log profile likelihood function over the given grid values of the time delay.

Details

The function entirelogprofilelikelihood is used to obtain the entire profile likelihood curve over the given grid values of the time delay.

References

Hyungsuk Tak, Kaisey Mandel, David A. van Dyk, Vinay L. Kashyap, Xiao-Li Meng, and Aneta Siemiginowska (in progress). Bayesian and Profile Likelihood Approaches to Time Delay Estimation for Stochastic Time Series of Gravitationally Lensed Quasars

Examples

  # Loading datasets
  data(simple)
  head(simple)

  ################################################
  # Time delay estimation via profile likelihood #
  ################################################


  ###### The entire profile likelihood values on the grid of values of the time delay.

  # Cubic microlensing model
  ti1 <- simple[, 1]
  ti2 <- simple[, 1]^2
  ti3 <- simple[, 1]^3
  ss <- lm(simple[, 4] - simple[, 2]~ ti1 + ti2 + ti3)

  initial <- c(mean(simple[, 2]), log(0.01), log(200), ss$coefficients)
  delta.uniform.range <- c(0, 100)
  grid <- seq(0, 100, by = 0.1) 
  # grid interval "by = 0.1" is recommended.

  ###  Running the following codes takes more time than CRAN policy
  ###  Please type the following lines without "#" to run the function and to see the results
  #  logprof <- entirelogprofilelikelihood(data = simple, grid = grid, 
  #                                        initial = initial, data.flux = FALSE, 
  #                                        delta.uniform.range = delta.uniform.range, micro = 3)

  #  plot(grid, logprof, type = "l", 
  #       xlab = expression(bold(Delta)),       
  #       ylab = expression(bold(paste("log L"[prof], "(", Delta, ")"))))
  #  prof <- exp(logprof - max(logprof))  # normalization
  #  plot(grid, prof, type = "l", 
  #       xlab = expression(bold(Delta)),       
  #       ylab = expression(bold(paste("L"[prof], "(", Delta, ")"))))