inst/notebook/2016-01-08-lognormal_calibration.md

In cboettig/multiple_uncertainty: Multiple Uncertainty

library("dplyr")
library("tidyr")
library("ggplot2")
library("multipleuncertainty")
knitr::opts_chunk$set(cache = TRUE)

Log-normal variance: (e^{\sigma^2-1} e^{2 \mu + \sigma^2}).

Uniform variance: (\frac{1}{12} (b-a)^2), where (b = \mu (1 + s)), (a = \mu (1 - s)), so (b - a = 2 mu * s), so variance is (\sigma^2 = \frac{\mu^2 s^2/3}). Rescaling units we can eliminate (\mu), and we're left with a more apples to apples comparison of comparable magnitudes of variance by taking (s = \sqrt{3} \sigma))

fig3 <- function(noise){  
  grid <- seq(0, 200, by=0.5)


  if(noise == "lognormal"){
    lo <- 0.0577 # 0.1 / sqrt(3)
    hi <- 0.2887 # 0.5 / sqrt(3)
  } else {
    lo <- 0.1
    hi <- 0.5
  }

  small     <- multiple_uncertainty(f = logistic, x_grid = grid, sigma_g = lo, sigma_m = lo, sigma_i = lo, noise_dist = noise)
  growth    <- multiple_uncertainty(f = logistic, x_grid = grid, sigma_g = hi, sigma_m = lo, sigma_i = lo, noise_dist = noise)
  measure   <- multiple_uncertainty(f = logistic, x_grid = grid, sigma_g = lo, sigma_m = hi, sigma_i = lo, noise_dist = noise)
  implement <- multiple_uncertainty(f = logistic, x_grid = grid, sigma_g = lo, sigma_m = lo, sigma_i = hi, noise_dist = noise)
  df <- data.frame(y_grid = grid, small = small, growth = growth, 
                   measure = measure, implement = implement) %>%
    tidyr::gather(scenario, value, -y_grid)
}

df <- 
data.frame(noise = c("uniform", "lognormal")) %>%
  dplyr::group_by(noise) %>%
  dplyr::do(fig3(.$noise))

df %>% ggplot(aes(x = y_grid, y = value, col = scenario)) + 
    geom_line()  + 
    facet_wrap(~ noise) + 
    xlab("Stock") + 
    ylab("Escapement") + 
    coord_cartesian(xlim = c(0, 150), ylim = c(0,100)) + 
    theme_bw()

Reed Result

reed <- multiple_uncertainty(noise_dist = "lognormal")

qplot(seq_along(reed), reed) + 
    coord_cartesian(xlim = c(0, 150), ylim = c(0, 150)) + 
    xlab("Stock") + ylab("Escapement") +
    theme_bw()

cboettig/multiple_uncertainty documentation built on May 13, 2019, 2:08 p.m.