ex1revdbayes.Rmd
in RstudioThere is further information in the Introduction to rust vignette.
# We need the rust and mvtnorm packages pkg <- c("rust", "mvtnorm") pkg_list <- pkg[!pkg %in% installed.packages()[, "Package"]] install.packages(pkg_list) # Load both packages invisible(lapply(pkg, library, character.only = TRUE))
# Information about the ru() function ?ru # Simulation sample size n <- 1000
# By default r = 1/2 # init is an initial estimate of the mode of logf x1 <- ru(logf = dnorm, log = TRUE, d = 1, n = n, init = 0.1) x1$pa plot(x1) # r = 1 will be slightly less efficient x2 <- ru(logf = dnorm, log = TRUE, d = 1, n = n, init = 0.1, r = 1) x2$pa
# lower = 0 tells ru() that the log-normal is bounded below at 0 x1 <- ru(logf = dlnorm, log = TRUE, d = 1, n = n, lower = 0, init = 1) x1$pa plot(x1) # We know that ln(X) is normal. # First transform using a Box-Cox transformation with lambda=0 then simulate lambda <- 0 x2 <- ru(logf = dlnorm, log = TRUE, d = 1, n = n, init = 0.1, trans = "BC", lambda = lambda) x2$pa # Plot the (normal) distribution from which we have simulated using ROU plot(x2, ru_scale = TRUE) # A check that the inverse (exponential) transformation has been applied plot(x2)
# two-dimensional normal with positive association ---------------- rho <- 0.9 covmat <- matrix(c(1, rho, rho, 1), 2, 2) x1 <- ru(logf = mvtnorm::dmvnorm, sigma = covmat, log = TRUE, d = 2, n = n, init = c(0, 0), rotate = FALSE) x2 <- ru(logf = mvtnorm::dmvnorm, sigma = covmat, log = TRUE, d = 2, n = n, init = c(0, 0), rotate = TRUE) c(x1$pa, x2$pa)
plot(x1, ru_scale = TRUE) plot(x2, ru_scale = TRUE)
# Exponential case, with strong skewness # A cube root transformation results in approximate symmetry alpha <- 1 x1 <- ru(logf = dgamma, shape = alpha, log = TRUE, d = 1, n = n, trans = "BC", lambda = 1/3, init = alpha) x1$pa # If alpha < 1 then the gamma density is extremely skewed and unbounded at 0 # A transformation can avoid this, but it needs to be stronger than a cube root alpha <- 0.1 x2 <- ru(logf = dgamma, shape = alpha, log = TRUE, d = 1, n = n, trans = "BC", lambda = 0.068, init = 0) x2$pa plot(x2) plot(x2, ru_scale = TRUE)
# Pick a standard distribution ?Distributions # Change dnorm to a d???? of your choice below # Perhaps also set lower, upper or init x <- ru(logf = dnorm, log = TRUE, n = n)
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