Rationale

Researchers have been interested in understanding the rate at which an area recovers after the forest has been clear cut because this has important implications for carbon storage and conservation more broadly. This recovery will often depend on site specific characteristics, such as soil fertility. In this example, we want to model how biomass recovery depends on both time and soil fertility. If we are successful at this task, we can potentially extrapolate our results to a much larger region to predict how much carbon can be sequestered if deforested areas are left to regenerate.

Data

I simulated some data “biomass recovery data.csv” and here is how these data look like:

setwd('U:\\uf\\courses\\bayesian course\\example biomass')
dat=read.csv('biomass recovery data.csv',as.is=T)
head(dat)

##   time    biomass Fertil site
## 1    1 0.03028436    0.1    1
## 2    2 0.60649551    0.1    1
## 3    5 0.23919867    0.1    1
## 4   10 0.06619132    0.1    1
## 5   20 0.17715621    0.1    1
## 6   40 0.43034782    0.1    1

plot(dat$time,dat$biomass,col=dat$site,xlab='Time (years)',ylab='Biomass',pch=19)

How should we go about modeling these data?

Here are some guiding questions:

• What mathematical function can we use to describe the pattern that we see from these data?
• What distribution can we use to represent the fact that there is some variability around the mathematical function described above?

For this assignment, we will first formulate a statistical model to then estimate its parameters using a Maximum Likelihood (MLE) approach. More specifically, after answering the questions above, we will need to:

• create a function that returns the loglikelihood based on a set of parameters
• use an optimizer to maximize the loglikelihood function that we created

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