## Probably the best PhD I’ll ever do

This is just the sort of qualified optimism I intend to carry all the way through my PhD (Photo courtesy of my friend Hugh Rabinovici).

I have done three interesting things in the past couple of months. I graduated from my Masters degree (stay tuned for the papers), moved from Melbourne, Australia to New York City, USA (don’t worry I’ll be back soon enough… maybe), and started my PhD.

My PhD: Learning, planning and decision making for vegetation management

Over the next few years I plan to tackle (other than crippling poverty)… Um… lots of things? Well, so far only one thing in particular.

Chapter 1: Value of information for Box Ironbark woodland management

My first chapter continues on from work colleagues and I published last year and which I blogged about a while back.

In this chapter I am undertaking a value of information analysis. In essence, a value of information analysis is a decision theoretic tool for assessing the cost effectiveness of doing science to aid decision making. The issue of doing science (or not) before making a decision has come up quite a bit lately. How often have you heard a politician say “before we do such-and-such, we need to find out more about such-and-such… blah, blah, blah”. I suspect they rarely stop to ask whether the ‘science’ needs to be done or even it is worth doing in the first place.

Central to a value of information analysis are the quantities expected value of sample information (EVSI) and expected net gain of sampling (ENGS). EVSI is the average gain you expect to achieve given you have performed an experiment (or made some observations) and are subsequently able to make a better decision. ENGS is then the difference between EVSI and the cost of obtaining the new information.

More formally, a value of information analysis asks: given a set, $A$, of possible, $a$, actions you could take, which could result (probabilistically) in any outcome, $\theta$, of a set of outcomes, $\Theta$, what is the value of performing an experiment, $e$, from a set of possible experiments, $E$, given the experiment could have any outcome $z$ from a set of experimental outcomes $Z$. In the mathematics of decision theory the aim is to maximise the utility function:

$u(e,z,a,\theta)$.

In other words, if you are faced with a decision problem under uncertainty what experiment should you undertake (which includes not doing any experiment at all) to maximize the difference between the change in your expected gain from taking an action and the cost of doing the experiment itself.

I am applying a value of information analysis to the management of Box Ironbark Woodlands. An objective of Victoria’s Box Ironbark Woodland managers is to improve the biodiversity value of the forests they manage. They have a number of management actions at their disposal, each of which has a different cost. But the effect of management, and the dynamics of the system itself, are highly uncertain. My aim is to help them decide whether doing experimental work to resolve some uncertainty is a cost-effective strategy that can aid them in achieving their objectives.