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#' tsd_MHmcmc runs the Metropolis-Hastings algorithm for tsd (Bayesian MCMC)
#' @title Metropolis-Hastings algorithm for Sex ratio
#' @author Marc Girondot \email{marc.girondot@@gmail.com}
#' @return A list with resultMCMC being mcmc.list object, resultLnL being likelihoods and parametersMCMC being the parameters used
#' @param n.iter Number of iterations for each step
#' @param parametersMCMC A set of parameters used as initial point for searching with information on priors
#' @param result An object obtained after a SearchR fit
#' @param n.chains Number of replicates
#' @param n.adapt Number of iterations before to store outputs
#' @param thin Number of iterations between each stored output
#' @param trace TRUE or FALSE or period, shows progress
#' @param traceML TRUE or FALSE to show ML
#' @param batchSize Number of observations to include in each batch fo SE estimation
#' @param adaptive Should an adaptive process for SDProp be used
#' @param adaptive.lag Lag to analyze the SDProp value in an adaptive content
#' @param adaptive.fun Function used to change the SDProp
#' @param filename If intermediate is not NULL, save intermediate result in this file
#' @param intermediate Period for saving intermediate result, NULL for no save
#' @param previous Previous result to be continued. Can be the filename in which intermediate results are saved.
#' @description Run the Metropolis-Hastings algorithm for tsd.\cr
#' Deeply modified from a MCMC script by Olivier Martin (INRA, Paris-Grignon).\cr
#' The number of iterations is n.iter+n.adapt+1 because the initial likelihood is also displayed.\cr
#' I recommend that thin=1 because the method to estimate SE uses resampling.\cr
#' If initial point is maximum likelihood, n.adapt = 0 is a good solution.\cr
#' To get the SE from result_mcmc <- tsd_MHmcmc(result=try), use:\cr
#' result_mcmc$BatchSE or result_mcmc$TimeSeriesSE\cr
#' The batch standard error procedure is usually thought to be not as accurate as the time series methods.\cr
#' Based on Jones, Haran, Caffo and Neath (2005), the batch size should be equal to sqrt(n.iter).\cr
#' Jones, G.L., Haran, M., Caffo, B.S. and Neath, R. (2006) Fixed Width Output Analysis for Markov chain Monte Carlo , Journal of the American Statistical Association, 101:1537-1547.\cr
#' coda package is necessary for this function.\cr
#' The parameters intermediate and filename are used to save intermediate results every 'intermediate' iterations (for example 1000). Results are saved in a file of name filename.\cr
#' The parameter previous is used to indicate the list that has been save using the parameters intermediate and filename. It permits to continue a mcmc search.\cr
#' These options are used to prevent the consequences of computer crash or if the run is very very long and processes at time limited.\cr
#' @family Functions for temperature-dependent sex determination
#' @examples
#' \dontrun{
#' library(embryogrowth)
#' eo <- subset(DatabaseTSD, Species=="Emys orbicularis", c("Males", "Females",
#' "Incubation.temperature"))
#' eo_logistic <- tsd(eo)
#' pMCMC <- tsd_MHmcmc_p(eo_logistic, accept=TRUE)
#' # Take care, it can be very long
#' result_mcmc_tsd <- tsd_MHmcmc(result=eo_logistic,
#' parametersMCMC=pMCMC, n.iter=10000, n.chains = 1,
#' n.adapt = 0, thin=1, trace=FALSE, adaptive=TRUE)
#' # summary() permits to get rapidly the standard errors for parameters
#' summary(result_mcmc_tsd)
#' plot(result_mcmc_tsd, parameters="S", scale.prior=TRUE, xlim=c(-3, 3), las=1)
#' plot(result_mcmc_tsd, parameters="P", scale.prior=TRUE, xlim=c(25, 35), las=1)
#'
#' plot(eo_logistic, resultmcmc = result_mcmc_tsd)
#'
#' 1-rejectionRate(as.mcmc(result_mcmc_tsd))
#' raftery.diag(as.mcmc(result_mcmc_tsd))
#' heidel.diag(as.mcmc(result_mcmc_tsd))
#' library(car)
#' o <- P_TRT(x=eo_logistic, resultmcmc=result_mcmc_tsd)
#' outEo <- dataEllipse(x=o$P_TRT[, "PT"],
#' y=o$P_TRT[, "TRT"],
#' levels=c(0.95),
#' draw=FALSE)
#' plot(x = o$P_TRT[, "PT"],
#' y=o$P_TRT[, "TRT"],
#' pch=".", las=1, bty="n",
#' xlab="Pivotal temperature",
#' ylab=paste0("TRT ", as.character(100*eo_logistic$l), "%"),
#' xlim=c(28.4, 28.6),
#' ylim=c(0.8, 1.8))
#' lines(outEo[, 1], outEo[, 2], col="green", lwd=2)
#' legend("topleft", legend = c("Emys orbicularis", "95% confidence ellipse"),
#' pch=c(19, NA), col=c("black", "green"), lty=c(0, 1), lwd=c(0, 2))
#'
#' logistic <- function(x, P, S) {
#' return(1/(1+exp((1/S)*(P-x))))
#' }
#'
#' q <- as.quantile(result_mcmc_tsd, fun=logistic,
#' xlim=seq(from=25, to=35, by=0.1), nameparxlim="x")
#' plot(x=seq(from=25, to=35, by=0.1), y=q[1, ], type="l", las=1,
#' xlab="Temperatures", ylab="Male proportion", bty="n")
#' lines(x=seq(from=25, to=35, by=0.1), y=q[2, ])
#'
#' }
#' @export
tsd_MHmcmc <- function(result=stop("A result of tsd() fit must be provided"), n.iter=10000,
parametersMCMC=NULL, n.chains = 1, n.adapt = 0,
thin=1, trace=FALSE, traceML=FALSE, batchSize=sqrt(n.iter),
adaptive=FALSE, adaptive.lag=500, adaptive.fun=function(x) {ifelse(x>0.234, 1.3, 0.7)},
intermediate=NULL, filename="intermediate.Rdata", previous=NULL) {
# result=eo_logistic; parametersMCMC=NULL;
# n.iter=10000; n.chains = 1; n.adapt = 0; thin=1; trace=TRUE; batchSize=sqrt(n.iter);intermediate=NULL; filename="intermediate.Rdata"; previous=NULL; adaptive=FALSE; adaptive.lag=500; adaptive.fun=function(x) {ifelse(x>0.234, 1.3, 0.7)}
if (is.character(previous)) {
itr <- NULL
load(previous)
previous <- itr
rm(itr)
print("Continue previous mcmc run")
} else {
print(parametersMCMC)
}
# 29/1/2014; Ajout de result$weight
# 30/1/2015 Ajout de fixedparameters
out <- MHalgoGen(n.iter=n.iter, parameters=parametersMCMC,
n.chains = n.chains, n.adapt = n.adapt, thin=thin,
trace=trace, traceML=traceML,
males=result$males, N=result$N, temperatures=result$temperatures,
equation=result$equation, fixed.parameters=result$fixed.parameters,
likelihood=getFromNamespace(".tsd_fit", ns="embryogrowth"),
parameters_name = "par",
adaptive=adaptive, adaptive.lag=adaptive.lag, adaptive.fun=adaptive.fun,
intermediate=intermediate, filename=filename, previous=previous)
fin <- try(summary(out), silent=TRUE)
if (batchSize>=n.iter/2) {
print("batchSize cannot be larger than half the number of iterations.")
rese <- rep(NA, dim(parametersMCMC)[1])
names(rese) <- rownames(parametersMCMC)
out <- c(out, SE=list(rese))
} else {
out <- c(out, BatchSE=list(coda::batchSE(out$resultMCMC, batchSize=batchSize)))
}
out$resultML <- result
out$equation <- result$equation
if (inherits(fin, "try-error")) {
lp <- rep(NA, nrow(out$parametersMCMC$parameters))
names(lp) <- rownames(out$parametersMCMC$parameters)
out <- c(out, TimeSeriesSE=list(lp))
out <- c(out, SD=list(lp))
} else {
out <- c(out, TimeSeriesSE=list(fin$statistics[,4]))
out <- c(out, SD=list(fin$statistics[,"SD"]))
}
out <- addS3Class(out, "mcmcComposite")
return(out)
}
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