# Random numbers based on Hessian matrix or MCMC If it is very long, use silent parameter to check if something goes wrong. If replicates is NULL or is 0, or if method is NULL, parameters are just copied into data.frame. ```r RandomFromHessianOrMCMC( se = NULL, Hessian = NULL, mcmc = NULL, chain = 1, regularThin = TRUE, MinMax = NULL, fitted.parameters = NULL, fixed.parameters = NULL, method = NULL, probs = c(0.025, 0.5, 0.975), replicates = 10000, fn = NULL, silent = FALSE, ParTofn = "par", ... ) ``` ## Arguments - `se`: A named vector with SE of parameters - `Hessian`: An Hessian matrix - `mcmc`: A result from MHalgogen() - `chain`: MCMC chain to be used - `regularThin`: If TRUE, use regular thin for MCMC - `MinMax`: A data.frame with at least two columns: Min and Max and rownames being the variable names - `fitted.parameters`: The fitted parameters - `fixed.parameters`: The fixed parameters - `method`: Can be NULL, "SE", "Hessian", "MCMC", or "PseudoHessianFromMCMC" - `probs`: Probability for quantiles - `replicates`: Number of replicates to generate the randoms - `fn`: The function to apply to each replicate - `silent`: Should the function display some information - `ParTofn`: Name of the parameter to send random values to fn - `...`: Parameters send to fn function ## Returns Returns a list with three data.frames named random, fn, and quantiles ## Details RandomFromHessianOrMCMC returns random numbers based on Hessian matrix or MCMC ## Examples ```r ## Not run: library(HelpersMG) val <- rnorm(100, mean=20, sd=5)+(1:100)/10 # Return -ln L of values in val in Gaussian distribution with mean and sd in par fitnorm <- function(par, data) { -sum(dnorm(data, par["mean"], abs(par["sd"]), log = TRUE)) } # Initial values for search p<-c(mean=20, sd=5) # fit the model result <- optim(par=p, fn=fitnorm, data=val, method="BFGS", hessian=TRUE) # Using Hessian df <- RandomFromHessianOrMCMC(Hessian=result$hessian, fitted.parameters=result$par, method="Hessian")$random hist(df[, 1], main="mean") hist(df[, 2], main="sd") plot(df[, 1], df[, 2], xlab="mean", ylab="sd", las=1, bty="n") # Using MCMC parameters_mcmc <- data.frame(Density=c('dnorm', 'dlnorm'), Prior1=c(10, 0.5), Prior2=c(2, 0.5), SDProp=c(0.35, 0.2), Min=c(-3, 0), Max=c(100, 10), Init=c(10, 2), stringsAsFactors = FALSE, row.names=c('mean', 'sd')) # Use of trace and traceML parameters # trace=1 : Only one likelihood is printed mcmc_run <- MHalgoGen(n.iter=50000, parameters=parameters_mcmc, data=val, parameters_name = "par", likelihood=fitnorm, n.chains=1, n.adapt=100, thin=1, trace=1) df <- RandomFromHessianOrMCMC(mcmc=mcmc_run, fitted.parameters=NULL, method="MCMC")$random hist(df[, 1], main="mean") hist(df[, 2], main="sd") plot(df[, 1], df[, 2], xlab="mean", ylab="sd", las=1, bty="n") # Using a function fn fitnorm <- function(par, data, x) { y=par["a"]*(x)+par["b"] -sum(dnorm(data, y, abs(par["sd"]), log = TRUE)) } p<-c(a=0.1, b=20, sd=5) # fit the model x <- 1:100 result <- optim(par=p, fn=fitnorm, data=val, x=x, method="BFGS", hessian=TRUE) # Using Hessian df <- RandomFromHessianOrMCMC(Hessian=result$hessian, fitted.parameters=result$par, method="Hessian", fn=function(par) (par["a"]*(x)+par["b"])) plot(1:100, val) lines(1:100, df$quantiles["50%", ]) lines(1:100, df$quantiles["2.5%", ], lty=2) lines(1:100, df$quantiles["97.5%", ], lty=2) ## End(Not run) ``` ## Author(s) Marc Girondot marc.girondot@gmail.com

RandomFromHessianOrMCMC function