In laurieKell/biodyn: Biomass Dynamic Model

library(knitr)

## Global options
options(max.print="75")
opts_chunk$set(fig.path="out/",
               echo=FALSE,
           cache=TRUE,
               cache.path="cache/",
               prompt=FALSE,
               tidy=TRUE,
               comment=NA,
               message=FALSE,
               warning=FALSE)
opts_knit$set(width=75)

Introduction

The bootstrap is a random resampling of data points (i.e a Monte Carlo simulation) from an original set of N points. It is assumed that the propbability of a data point being chosen is $1//N$ and is independent of it having been chosen previously. A given data point $x_i$ will on average appear once, but it may appear never or twice, and so on in any Monte Carlo generated data set. The probability that $x_i$ appears $n_i$ times approximates to a Poisson distribution with a mean of 1.

However, it is not exactly Poissonian because of the constraint in Eq. (34) below. It turns out that we shall need to include the devition from Poisson distribution even for large N. We shall use the term ???bootstrap??? data sets to denote the Monte Carlo-generat ed data sets. More precisely, let us suppose that the number of times xi appears in a Monte Carlo-generated data set is ni. Since each bootstrap dataset contains exactly N data points, we have the constrain

Simulations

library(biodyn)
library(ggplotFL)

bd=sim()
bd=window(bd,end=49)

cpue=(stock(bd)[,-dims(bd)$year]+stock(bd)[,-1])/2
cpue=rlnorm(250,log(cpue),.2)

plot(cpue)

#set parameters
setParams(bd) =cpue
setControl(bd)=params(bd)
control(bd)[3:4,"phase"]=-1

#fit
catch(bd)=propagate(catch(bd),250)
bdHat=fit(bd,cpue)

plot(biodyns("Hat"=bdHat,"True"=bd))

median(stock(bd)[,49])
median(stock(bdHat)[,49])