1d:T793,# iterLap package information Implementation of iterLap package ## Details This package implements the multiple mode Laplace approximation by Gelman and Rubin (via function GRApprox) and the iterated Laplace approximation (via the function iterLap). Both functions return objects of class mixDist, which contain the fitted mode vectors and covariance matrices. Print and summary methods exist to display the contents of a mixDist object in human-readable form. Function IS performs importance sampling, using a mixDist object as input parameter. ## Author(s) Bjoern Bornkamp Maintainer: Bjoern Bornkamp ## References Bornkamp, B. (2011). Approximating Probability Densities by Iterated Laplace Approximations, **Journal of Computational and Graphical Statistics**, 20 (3), 656--669. ## Examples ```r ## banana example banana <- function(pars, b, sigma12){ dim <- 10 y <- c(pars[1], pars[2]+b*(pars[1]^2-sigma12), pars[3:dim]) cc <- c(1/sqrt(sigma12), rep(1, dim-1)) return(-0.5*sum((y*cc)^2)) } start <- rbind(rep(0,10),rep(-1.5,10),rep(1.5,10)) ## multiple mode Laplace approximation gr <- GRApprox(banana, start, b = 0.03, sigma12 = 100) ## print mixDist object gr ## summary method summary(gr) ## importance sampling using the obtained mixDist object ## using a mixture of t distributions with 10 degrees of freedom issamp <- IS(gr, nSim=1000, df = 10, post=banana, b = 0.03, sigma12 = 100) ## effective sample size issamp$ESS ## now use iterated Laplace approximation (using gr mixDist object ## from above as starting approximation) iL <- iterLap(banana, GRobj = gr, b = 0.03, sigma12 = 100) ISObj <- IS(iL, nSim=10000, df = 100, post=banana, b = 0.03, sigma12 = 100) ## residual resampling to obtain unweighted sample sims <- resample(1000, ISObj) plot(sims[,1], sims[,2], xlim=c(-40,40), ylim = c(-40,20)) ```

iterLap-package