R/Est_max_LnL.R
In tylerhether/fbgenotyper: R package using the Forward-Backward algorithm to infer genotypes, recombination hotspots, and gene conversion tracts from low-coverage next-generation sequence data
#' @title Numerically Estimating the Maximum LnL parameter values from the data
#'
#' @description Infers the genome-wide recombination rate (Morgans / bp) and the assignment
#' probabilty directly from the data using maximum likelihood estimates.
#'
#' @param dat a data.frame with five columns:
#' \itemize{
#' \item \code{Ind}{ The individual ID}
#' \item \code{Chr}{ The chromosome ID}
#' \item \code{Snp}{ The (sorted) snp location (in bps)}
#' \item \code{p0}{ The number of reads that mapped to parent 0}
#' \item \code{p1}{ The number of reads that mapped to parent 1}
#' }
#' Note that the names of the columns can be different and there can be additional columns to the right (\code{est_maxLnL} only uses the
#' first 5 columns of the data.frame).
#'
#' @param \code{ploidy} The ploidy to analyze. If \code{ploidy="diploid"} (default) then
#' \code{\link{fb_diploid}} is used to infer states and estimate likelihood. If \code{ploidy="haploid"}
#' then \code{\link{fb_haploid}} will be used.
#'
#' @param \code{initial_p_assign} The initial assignment probability (see details). If "NULL" (default), then a coarse search will be performed with
#' \code{n_coarse_steps} equally spaced from 0.95 to 0.999.
#'
#' @param \code{initial_scale} The initial genome-wide recombination rate (Morgans / bp).
#' If "NULL" (default), then a coarse search will be performed \code{n_coarse_steps} equally spaced from
#' 1e-06 to 1e-04.
#'
#' @param \code{tolerance} The tolerance used to stop the search.
#'
#' @param \code{n_coarse_steps} The size of the 1D (if either \code{initial_p_assign} or \code{initial_scale} is "NULL") or
#' 2D grid (if both are "NULL"). Increasing \code{n_coarse_steps} can greatly increase computation time.
#'
#' @param \code{n_iterations} The number of iterations during the fine scale parameter estimate serach (see details).
#'
#' @param \code{n_cores} Integer specifying the number of processors to use
#'
#' @details \code{est_maxLnL} has a coarse and fine scale method to estimate
#' the genome-wide recombination rate, \eqn{\hat{c}}, and assignement probability, \eqn{\hat{p}}.
#' The coarse scale uses either \code{fb_haploid} or \code{fb_diploid} output and estimates
#' the natural log-likelihood, LnL, of the data across a coarse (in parameter space) grid of varying
#' \eqn{p} or \eqn{c} values and the fine scale uses a two-variable Newton-Raphson method to hone
#' in on a closer estimate. For further details see Hether et al. (in prep).
#'
#' @return A data.frame containing the following columns:
#' \itemize{
#' \item{p_assign_hat}{ An estimate of the assignment probability}
#' \item{scale_hat}{ An estimate of mean recombination rate}
#' \item{n_iterations}{ The number of iterations carried out}
#' }
#'
#' @references Hether, T.D., C. G. Wiench1, and P.A. Hohenlohe (in review). 2015. Novel molecular and analytical tools
#' for efficient estimation of rates of meiotic crossover, non-crossover and gene conversion
#'
#' P. Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms. Springer
#' Series in Computational Mathematics, Vol. 35. Springer, Berlin, 2004.
#'
#' @seealso \code{\link{fb_haploid}}, \code{\link{fb_haploid}}
#'
#' @author Tyler D. Hether
#'
#' @export est_maxLnL
#'
#' @examples
#' # Simulating 30 haploid recombinants
#' set.seed(1234567) # For reproducibility
#' n_spores <- 30 # number of recombinants
#' l <- 1000 # number of snps to simulate
#' c <- 1e-06 # recombination rate between snps (Morgan/bp)
#' snps <- c(1:l)*1e2 # snps are evenly spaced 100bps apart
#' p_a <- 0.985 # assignment probability
#' coverage <- 1 # mean coverage
#' # Now simulate
#' sim <- sim_en_masse(n.spores=n_spores, scale=c, snps=snps,
#' p.assign=p_a, mu.rate=0, f.cross=1, f.convert=0,
#' length.conversion=0, coverage=coverage)
#' # Now estmate params
#' res <- est_maxLnL(sim, ploidy="haploid", plot=TRUE, n_cores=5)
#' res
#' @export est_maxLnL
est_maxLnL <- function(dat, ploidy="haploid", initial_p_assign="NULL", initial_scale="NULL", tolerance=1e-03, n_coarse_steps=5, n_iterations=30, plot=FALSE, n_cores=1)
{
# print(sessionInfo())
# initial iteration
n = 0
# This is the tolerance. If the estimates of x1 and y1 are
# less than tol distance apart than stop the algorithm
tol <- tolerance
# diff is the difference in lnl between the old and new values.
# It is initially larger than tol
diff <- 1
# dx is the distance between the focal x1 point and points x0 or x2
# where x is the p_assign parameter that is to be estimated
dx <- dx_master <- 1e-04
# dy is the distancw between the focal y1 point and points y0 or y2
# where y is the scale parameter that is to be estimated
dy <- dy_master <- 1e-05
x <- initial_p_assign; y <- initial_scale # (x,y) is the starting (p_assign, scale) point for the algorithm.
# dat is a df with 5 columns: "Ind", "Chr", "Snp", "p0", "p1"
colnames(dat) <- c("Ind", "Chr", "Snp", "p0", "p1")
dat <- dat[,1:5]
# If x or y == NULL, do a coarse scale grid to estimate appropriate starting values.
# This is either a 5 point 1D grid (if either x or y is NULL) or a 5x5 2D grid if
# both x and y are NULL.
if(x=="NULL" || y=="NULL")
{
if(x=="NULL")
{
x <- seq(from=0.95, to=0.999, length.out=n_coarse_steps)
}
if(y=="NULL")
{
y <- seq(from=1e-06, to=1e-04, length.out=n_coarse_steps)
}
pars <- expand.grid(x=x, y=y) # This is the grid
# Define the number of cores to use for parallel computing
cl <- parallel::makeCluster(n_cores)
# Register cluster
parallel::clusterExport(cl, varlist=ls(), envir=environment())
# Estimate the most likely set of starting values
coarse_res <- parallel::parLapply(cl, 1:dim(pars)[1], function(yy){
require(plyr)
require(HMMancestry)
res_c <- plyr::ddply(dat, .(Ind, Chr), function(xx){
if(ploidy=="haploid")
{
return(HMMancestry::fb_haploid(xx[,3], xx[,4], xx[,5], pars[yy,1], pars[yy,2]))
}
if(ploidy=="diploid")
{
return(HMMancestry::fb_diploid(xx[,3], xx[,4], xx[,5], pars[yy,1], pars[yy,2]))
}
})
# Return the lnL for each unique tetrad, spore, & chr
res_lnl <- plyr::ddply(res_c, .(Ind, Chr), function(z){
return(z$lnL[1])
})
return(data.frame(p_assign=pars[yy,1], scale=pars[yy,2], lnL=res_lnl))
})
parallel::stopCluster(cl)
LnL <- unlist(lapply(coarse_res, function(x){
return(sum(x$lnL.V1))
}))
# The maximum likelihood estimate for p_assign and scale are:
MAX <- head(coarse_res[[which(LnL==max(LnL))]])[1,1:2]
print(paste("Coarse estimates are ", MAX[1], " and ", MAX[2], sep=""))
x <- as.numeric(MAX[1])
y <- as.numeric(MAX[2])
# For visualizing:
if(plot==TRUE)
{
LnL <- data.frame(p_assign=pars[,1],scale=pars[,2],LnL)
if(initial_p_assign=="NULL" && initial_scale!="NULL")
{
print(plot(LnL$p_assign, LnL$LnL, type="b", xlab="p_assign", ylab=paste("LnL given scale = ", y, sep="")))
}
if(initial_p_assign!="NULL" && initial_scale=="NULL")
{
print(plot(LnL$scale, LnL$LnL, type="b", xlab="scale", ylab=paste("LnL given p_assign = ", x, sep="")))
}
if(initial_p_assign=="NULL" && initial_scale=="NULL")
{
print(lattice::contourplot(LnL~p_assign*scale, data=LnL, region=TRUE, cuts=6))
}
}
}
# Perform the hill climbing procedure to fine-tune the parameters
repeat{
if(n_iterations==0) break
n <- n + 1
print(paste("Processing iteration ", n, " out of a max of ", n_iterations, ".",sep=""))
dx <- dx_master/n
dy <- dy_master/n
# print(n)
# For each iteration there are 6 (p_assign, scale) points that need estimated lnls
# before a jump can be proposed. These points are below. Note that
# x is bounded between 0.5 and 1 (exclusive) and
# y must always be positive.
points <- list(
"x0y0" = c(max((x-dx), 0.50000001),max((y-dy), 1e-09)),
"x1y0" = c(x, max((y-dy), 1e-09)),
"x0y1" = c(max((x-dx), 0.50000001),y),
"x1y1" = c(x,y),
"x2y1" = c(min((x+dx), 0.99999999),y),
"x1y2" = c(x, (y+dy))
)
# Define the number of cores to use for parallel computing
cl <- parallel::makeCluster(n_cores)
# Register cluster
parallel::clusterExport(cl, varlist=ls(), envir=environment())
lnls <- parallel::parLapply(cl, points, function(fun){
require(plyr)
require(HMMancestry)
# Call the hmm and get the lnl for each unique individual by chromosome combination
res_c <- plyr::ddply(dat[,c(1:5)], .(Ind, Chr), function(xx){
if(ploidy=="haploid")
{
return(HMMancestry::fb_haploid(xx[,3], xx[,4], xx[,5], fun[1], fun[2]))
}
if(ploidy=="diploid")
{
return(HMMancestry::fb_diploid(xx[,3], xx[,4], xx[,5], fun[1], fun[2]))
}
})
# Return the lnL for each unique individual and chromosome
res_lnl <- plyr::ddply(res_c, .(Ind, Chr), function(z){
return(z$lnL[1])
})
# Sum over the above lnl to get the total lnl for all data
lnl <- sum(res_lnl$V1)
return(lnl)
})
parallel::stopCluster(cl)
# Here's the Hessian matrix
H <- matrix(c(
(lnls$x0y1 + lnls$x2y1 -2*lnls$x1y1)/(dx*dx),
(lnls$x0y0 + lnls$x1y1 - lnls$x0y1 - lnls$x1y0)/(dx*dy),
(lnls$x0y0 + lnls$x1y1 - lnls$x0y1 - lnls$x1y0)/(dx*dy),
(lnls$x1y0 + lnls$x1y2 -2*lnls$x1y1)/(dy*dy)
),2,2,byrow=TRUE)
# Here's the gradient
Grad <- c(
(lnls$x2y1 - lnls$x1y1)/dx,
(lnls$x1y2 - lnls$x1y1)/dy
)
# The new x,y point
xy <- c(x,y) - solve(H)%*%Grad
# x and y are bounded: x between 0.5 and 1 (exclusive) and y between 0 and 1.
# Adjust the new xy point if needed to their dx (dy) displacements:
if(xy[1]<=0.5)
{
xy[1] = max(x-1e-06, 0.50001)
}
if(xy[1]>=1)
{
xy[1] = min(x+1e-06, 0.9999)
}
if(xy[2]<=0)
{
xy[2] = max(y-1e-06, 0.00001)
}
if(xy[2]>=1)
{
xy[2] = min(y+1e-06, 0.9999)
}
# print(xy)
# See if the new xy point has a higher lnl than all 6 points.
# If it is greater, accept the move.
new_xy_lnl <- plyr::ddply(dat[,c(1:5)], .(Ind, Chr), function(xx){
if(ploidy=="haploid")
{
return(fb_haploid(xx[,3], xx[,4], xx[,5], xy[1], xy[2]))
}
if(ploidy=="diploid")
{
return(fb_diploid(xx[,3], xx[,4], xx[,5], xy[1], xy[2]))
}
})
# Return the lnL for each unique individual and chromosome
res_new_lnl <- plyr::ddply(new_xy_lnl, .(Ind, Chr), function(z){
return(z$lnL[1])
})
# Sum over the above lnl to get the total lnl for all data
new_lnl <- sum(res_new_lnl$V1)
# Troubleshooting:
# xs <- c(lapply(points, "[", 1L), xy[1]); ys <- c(lapply(points, "[", 2L), xy[2]); DAT <- data.frame(xs=unlist(xs), ys=unlist(ys), l=as.numeric(c(unlist(lnls), new_lnl))); ggplot(data=DAT, aes(x=xs, y=ys, colour=factor(l))) + geom_point()
# Is the new xy's lnl > all 6 points? If so, accept it.
if(new_lnl > rev(sort(unlist(lnls)))[1])
{
# The Euclidean distance between the old and new point is:
diff <- dist(matrix(c(x,y,xy[1],xy[2]),2,2, byrow=TRUE))
} else {
# If one or more of the 6 points have a greater lnl than the
# proposed xy point, then pick the point with the highest lnl
# xy <- points[[as.numeric(which(unlist(lnls)==max(unlist(lnls))))]]
xy <- points[[names(rev(sort(unlist(lnls)))[1])]]
# print("One of the 6 points has a greater lnl than the proposed point")
}
# Update parameters
x <- xy[1]
y <- xy[2]
# Stop the algorithm if the number of iterations is exceeded or
# the max lnl values do not change much (within tolerance)
if(n==n_iterations || diff<tol)
{
if(n==n_iterations)
{
print(paste("maximum lnl estimate not reached after ", n, " iterations", sep=""))
break
}
print(paste("maximum lnl estimate reached after ", n, " iterations", sep=""))
break
}
}
return(data.frame(p_assign_hat=xy[1], scale_hat=xy[2],n_iterations=n))
}
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#' @title Numerically Estimating the Maximum LnL parameter values from the data
#'
#' @description Infers the genome-wide recombination rate (Morgans / bp) and the assignment
#' probabilty directly from the data using maximum likelihood estimates.
#'
#' @param dat a data.frame with five columns:
#' \itemize{
#' \item \code{Ind}{ The individual ID}
#' \item \code{Chr}{ The chromosome ID}
#' \item \code{Snp}{ The (sorted) snp location (in bps)}
#' \item \code{p0}{ The number of reads that mapped to parent 0}
#' \item \code{p1}{ The number of reads that mapped to parent 1}
#' }
#' Note that the names of the columns can be different and there can be additional columns to the right (\code{est_maxLnL} only uses the
#' first 5 columns of the data.frame).
#'
#' @param \code{ploidy} The ploidy to analyze. If \code{ploidy="diploid"} (default) then
#' \code{\link{fb_diploid}} is used to infer states and estimate likelihood. If \code{ploidy="haploid"}
#' then \code{\link{fb_haploid}} will be used.
#'
#' @param \code{initial_p_assign} The initial assignment probability (see details). If "NULL" (default), then a coarse search will be performed with
#' \code{n_coarse_steps} equally spaced from 0.95 to 0.999.
#'
#' @param \code{initial_scale} The initial genome-wide recombination rate (Morgans / bp).
#' If "NULL" (default), then a coarse search will be performed \code{n_coarse_steps} equally spaced from
#' 1e-06 to 1e-04.
#'
#' @param \code{tolerance} The tolerance used to stop the search.
#'
#' @param \code{n_coarse_steps} The size of the 1D (if either \code{initial_p_assign} or \code{initial_scale} is "NULL") or
#' 2D grid (if both are "NULL"). Increasing \code{n_coarse_steps} can greatly increase computation time.
#'
#' @param \code{n_iterations} The number of iterations during the fine scale parameter estimate serach (see details).
#'
#' @param \code{n_cores} Integer specifying the number of processors to use
#'
#' @details \code{est_maxLnL} has a coarse and fine scale method to estimate
#' the genome-wide recombination rate, \eqn{\hat{c}}, and assignement probability, \eqn{\hat{p}}.
#' The coarse scale uses either \code{fb_haploid} or \code{fb_diploid} output and estimates
#' the natural log-likelihood, LnL, of the data across a coarse (in parameter space) grid of varying
#' \eqn{p} or \eqn{c} values and the fine scale uses a two-variable Newton-Raphson method to hone
#' in on a closer estimate. For further details see Hether et al. (in prep).
#'
#' @return A data.frame containing the following columns:
#' \itemize{
#' \item{p_assign_hat}{ An estimate of the assignment probability}
#' \item{scale_hat}{ An estimate of mean recombination rate}
#' \item{n_iterations}{ The number of iterations carried out}
#' }
#'
#' @references Hether, T.D., C. G. Wiench1, and P.A. Hohenlohe (in review). 2015. Novel molecular and analytical tools
#' for efficient estimation of rates of meiotic crossover, non-crossover and gene conversion
#'
#' P. Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms. Springer
#' Series in Computational Mathematics, Vol. 35. Springer, Berlin, 2004.
#'
#' @seealso \code{\link{fb_haploid}}, \code{\link{fb_haploid}}
#'
#' @author Tyler D. Hether
#'
#' @export est_maxLnL
#'
#' @examples
#' # Simulating 30 haploid recombinants
#' set.seed(1234567) # For reproducibility
#' n_spores <- 30 # number of recombinants
#' l <- 1000 # number of snps to simulate
#' c <- 1e-06 # recombination rate between snps (Morgan/bp)
#' snps <- c(1:l)*1e2 # snps are evenly spaced 100bps apart
#' p_a <- 0.985 # assignment probability
#' coverage <- 1 # mean coverage
#' # Now simulate
#' sim <- sim_en_masse(n.spores=n_spores, scale=c, snps=snps,
#' p.assign=p_a, mu.rate=0, f.cross=1, f.convert=0,
#' length.conversion=0, coverage=coverage)
#' # Now estmate params
#' res <- est_maxLnL(sim, ploidy="haploid", plot=TRUE, n_cores=5)
#' res
#' @export est_maxLnL
est_maxLnL <- function(dat, ploidy="haploid", initial_p_assign="NULL", initial_scale="NULL", tolerance=1e-03, n_coarse_steps=5, n_iterations=30, plot=FALSE, n_cores=1)
{
# print(sessionInfo())
# initial iteration
n = 0
# This is the tolerance. If the estimates of x1 and y1 are
# less than tol distance apart than stop the algorithm
tol <- tolerance
# diff is the difference in lnl between the old and new values.
# It is initially larger than tol
diff <- 1
# dx is the distance between the focal x1 point and points x0 or x2
# where x is the p_assign parameter that is to be estimated
dx <- dx_master <- 1e-04
# dy is the distancw between the focal y1 point and points y0 or y2
# where y is the scale parameter that is to be estimated
dy <- dy_master <- 1e-05
x <- initial_p_assign; y <- initial_scale # (x,y) is the starting (p_assign, scale) point for the algorithm.
# dat is a df with 5 columns: "Ind", "Chr", "Snp", "p0", "p1"
colnames(dat) <- c("Ind", "Chr", "Snp", "p0", "p1")
dat <- dat[,1:5]
# If x or y == NULL, do a coarse scale grid to estimate appropriate starting values.
# This is either a 5 point 1D grid (if either x or y is NULL) or a 5x5 2D grid if
# both x and y are NULL.
if(x=="NULL" || y=="NULL")
{
if(x=="NULL")
{
x <- seq(from=0.95, to=0.999, length.out=n_coarse_steps)
}
if(y=="NULL")
{
y <- seq(from=1e-06, to=1e-04, length.out=n_coarse_steps)
}
pars <- expand.grid(x=x, y=y) # This is the grid
# Define the number of cores to use for parallel computing
cl <- parallel::makeCluster(n_cores)
# Register cluster
parallel::clusterExport(cl, varlist=ls(), envir=environment())
# Estimate the most likely set of starting values
coarse_res <- parallel::parLapply(cl, 1:dim(pars)[1], function(yy){
require(plyr)
require(HMMancestry)
res_c <- plyr::ddply(dat, .(Ind, Chr), function(xx){
if(ploidy=="haploid")
{
return(HMMancestry::fb_haploid(xx[,3], xx[,4], xx[,5], pars[yy,1], pars[yy,2]))
}
if(ploidy=="diploid")
{
return(HMMancestry::fb_diploid(xx[,3], xx[,4], xx[,5], pars[yy,1], pars[yy,2]))
}
})
# Return the lnL for each unique tetrad, spore, & chr
res_lnl <- plyr::ddply(res_c, .(Ind, Chr), function(z){
return(z$lnL[1])
})
return(data.frame(p_assign=pars[yy,1], scale=pars[yy,2], lnL=res_lnl))
})
parallel::stopCluster(cl)
LnL <- unlist(lapply(coarse_res, function(x){
return(sum(x$lnL.V1))
}))
# The maximum likelihood estimate for p_assign and scale are:
MAX <- head(coarse_res[[which(LnL==max(LnL))]])[1,1:2]
print(paste("Coarse estimates are ", MAX[1], " and ", MAX[2], sep=""))
x <- as.numeric(MAX[1])
y <- as.numeric(MAX[2])
# For visualizing:
if(plot==TRUE)
{
LnL <- data.frame(p_assign=pars[,1],scale=pars[,2],LnL)
if(initial_p_assign=="NULL" && initial_scale!="NULL")
{
print(plot(LnL$p_assign, LnL$LnL, type="b", xlab="p_assign", ylab=paste("LnL given scale = ", y, sep="")))
}
if(initial_p_assign!="NULL" && initial_scale=="NULL")
{
print(plot(LnL$scale, LnL$LnL, type="b", xlab="scale", ylab=paste("LnL given p_assign = ", x, sep="")))
}
if(initial_p_assign=="NULL" && initial_scale=="NULL")
{
print(lattice::contourplot(LnL~p_assign*scale, data=LnL, region=TRUE, cuts=6))
}
}
}
# Perform the hill climbing procedure to fine-tune the parameters
repeat{
if(n_iterations==0) break
n <- n + 1
print(paste("Processing iteration ", n, " out of a max of ", n_iterations, ".",sep=""))
dx <- dx_master/n
dy <- dy_master/n
# print(n)
# For each iteration there are 6 (p_assign, scale) points that need estimated lnls
# before a jump can be proposed. These points are below. Note that
# x is bounded between 0.5 and 1 (exclusive) and
# y must always be positive.
points <- list(
"x0y0" = c(max((x-dx), 0.50000001),max((y-dy), 1e-09)),
"x1y0" = c(x, max((y-dy), 1e-09)),
"x0y1" = c(max((x-dx), 0.50000001),y),
"x1y1" = c(x,y),
"x2y1" = c(min((x+dx), 0.99999999),y),
"x1y2" = c(x, (y+dy))
)
# Define the number of cores to use for parallel computing
cl <- parallel::makeCluster(n_cores)
# Register cluster
parallel::clusterExport(cl, varlist=ls(), envir=environment())
lnls <- parallel::parLapply(cl, points, function(fun){
require(plyr)
require(HMMancestry)
# Call the hmm and get the lnl for each unique individual by chromosome combination
res_c <- plyr::ddply(dat[,c(1:5)], .(Ind, Chr), function(xx){
if(ploidy=="haploid")
{
return(HMMancestry::fb_haploid(xx[,3], xx[,4], xx[,5], fun[1], fun[2]))
}
if(ploidy=="diploid")
{
return(HMMancestry::fb_diploid(xx[,3], xx[,4], xx[,5], fun[1], fun[2]))
}
})
# Return the lnL for each unique individual and chromosome
res_lnl <- plyr::ddply(res_c, .(Ind, Chr), function(z){
return(z$lnL[1])
})
# Sum over the above lnl to get the total lnl for all data
lnl <- sum(res_lnl$V1)
return(lnl)
})
parallel::stopCluster(cl)
# Here's the Hessian matrix
H <- matrix(c(
(lnls$x0y1 + lnls$x2y1 -2*lnls$x1y1)/(dx*dx),
(lnls$x0y0 + lnls$x1y1 - lnls$x0y1 - lnls$x1y0)/(dx*dy),
(lnls$x0y0 + lnls$x1y1 - lnls$x0y1 - lnls$x1y0)/(dx*dy),
(lnls$x1y0 + lnls$x1y2 -2*lnls$x1y1)/(dy*dy)
),2,2,byrow=TRUE)
# Here's the gradient
Grad <- c(
(lnls$x2y1 - lnls$x1y1)/dx,
(lnls$x1y2 - lnls$x1y1)/dy
)
# The new x,y point
xy <- c(x,y) - solve(H)%*%Grad
# x and y are bounded: x between 0.5 and 1 (exclusive) and y between 0 and 1.
# Adjust the new xy point if needed to their dx (dy) displacements:
if(xy[1]<=0.5)
{
xy[1] = max(x-1e-06, 0.50001)
}
if(xy[1]>=1)
{
xy[1] = min(x+1e-06, 0.9999)
}
if(xy[2]<=0)
{
xy[2] = max(y-1e-06, 0.00001)
}
if(xy[2]>=1)
{
xy[2] = min(y+1e-06, 0.9999)
}
# print(xy)
# See if the new xy point has a higher lnl than all 6 points.
# If it is greater, accept the move.
new_xy_lnl <- plyr::ddply(dat[,c(1:5)], .(Ind, Chr), function(xx){
if(ploidy=="haploid")
{
return(fb_haploid(xx[,3], xx[,4], xx[,5], xy[1], xy[2]))
}
if(ploidy=="diploid")
{
return(fb_diploid(xx[,3], xx[,4], xx[,5], xy[1], xy[2]))
}
})
# Return the lnL for each unique individual and chromosome
res_new_lnl <- plyr::ddply(new_xy_lnl, .(Ind, Chr), function(z){
return(z$lnL[1])
})
# Sum over the above lnl to get the total lnl for all data
new_lnl <- sum(res_new_lnl$V1)
# Troubleshooting:
# xs <- c(lapply(points, "[", 1L), xy[1]); ys <- c(lapply(points, "[", 2L), xy[2]); DAT <- data.frame(xs=unlist(xs), ys=unlist(ys), l=as.numeric(c(unlist(lnls), new_lnl))); ggplot(data=DAT, aes(x=xs, y=ys, colour=factor(l))) + geom_point()
# Is the new xy's lnl > all 6 points? If so, accept it.
if(new_lnl > rev(sort(unlist(lnls)))[1])
{
# The Euclidean distance between the old and new point is:
diff <- dist(matrix(c(x,y,xy[1],xy[2]),2,2, byrow=TRUE))
} else {
# If one or more of the 6 points have a greater lnl than the
# proposed xy point, then pick the point with the highest lnl
# xy <- points[[as.numeric(which(unlist(lnls)==max(unlist(lnls))))]]
xy <- points[[names(rev(sort(unlist(lnls)))[1])]]
# print("One of the 6 points has a greater lnl than the proposed point")
}
# Update parameters
x <- xy[1]
y <- xy[2]
# Stop the algorithm if the number of iterations is exceeded or
# the max lnl values do not change much (within tolerance)
if(n==n_iterations || diff<tol)
{
if(n==n_iterations)
{
print(paste("maximum lnl estimate not reached after ", n, " iterations", sep=""))
break
}
print(paste("maximum lnl estimate reached after ", n, " iterations", sep=""))
break
}
}
return(data.frame(p_assign_hat=xy[1], scale_hat=xy[2],n_iterations=n))
}
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