By Wai Pun, The University of Adelaide
As implied by the topic, statistical decision theory is about making decisions under uncertainty. In Decision Theory, we wish to choose the action that leads to the most desirable outcome. Such a framework is often applied in areas such as public policy, management and clinical trials. This project focuses on the basic concepts of Decision Theory such as identifying the risk of an action, inference for uncertainty and setting up the optimal decision rule.
Let’s start with an example. A drug company wants to produce the right quantity of a drug for the market to maximise their profit. However, we don’t know the true market demand. This uncertainty greatly affects the company’s profit. The consequences of over-production and under-production can be different. We need to identify the impact on the profit if our production mismatches the market demand.
What we can do is an experiment to better understand the demand. The data collected from this experiment will be analysed using Bayesian statistics. The idea of Bayesian statistics is that we start with a belief about the demand, called the prior distribution. After the experiment, we use the observed data to improve our understanding about the demand. The demand will then be interpreted as a probability model, known as the posterior distribution. With more data, the posterior distribution can more accurately predict the market demand and it is easier for us to calculate how much to produce.
In decision theory, we would also like to construct a general decision rule that we can use to suggest an action to take for any given situation. Our goal is to find the optimal decision rule such that it gives the action that leads to the least risk in any case. However, constructing the optimal decision rule is not an easy talk because we can have an infinite choice of decision rules. Through Bayesian analysis, the optimal decision rule can be obtained using the posterior distribution.
This framework can be extended to solve more decision-making problems. The topic of my honours project will be to analyse a dataset of mice with gastric cancer collected by the Adelaide Proteomics Centre. Applying the ideas of Statistical Decision Theory, we will decide how to handle the missing values in replicated mass spectra of mice. This will involve the study of hierarchical models to handle the multi-level structure of the data.
I would like to thank my supervisor, Professor Patty Solomon. Without her guidance, I could not have completed the project to this standard. Also, I would like to thank the Australian Mathematical Sciences Institute and the University of Adelaide for the invaluable research experience and the scholarship.
Wai Pun was one of the recipients of a 2013/14 AMSI Vacation Research Scholarship.