Optimal static and sequential design : a critical review

The aim of this thesis is to review and augment the theory and methods of optimal experimental design. In Chapter I the scene is set by considering the possible aims of an experimenter prior to an experiment, the statistical methods one might use to achieve those aims and how experimental design might aid this procedure. It is indicated that, given a criterion for design, a priori optimal design will only be possible in certain instances and, otherwise, some form of sequential procedure would seem to be indicated. In Chapter 2 an exact experimental design problem is formulated mathematically and is compared with its continuous analogue. Motivation is provided for the solution of this continuous problem, and the remainder of the chapter concerns this problem. A necessary and sufficient condition for optimality of a design measure is given. Problems which might arise in testing this condition are discussed, in particular with respect to possible non-differentiability of the criterion function at the design being tested. Several examples are given of optimal designs which may be found analytically and which illustrate the points discussed earlier in the chapter. In Chapter 3 numerical methods of solution of the continuous optimal design problem are reviewed. A new algorithm is presented with illustrations of how it should be used in practice. It is shown that, for reasonably large sample size, continuously optimal designs may be approximated to well by an exact design. In situations where this is not satisfactory algorithms for improvement of this design are reviewed. Chapter 4 consists of a discussion of sequentially designed experiments, with regard to both the philosophies underlying, and the application of the methods of, statistical inference. In Chapter 5 we criticise constructively previous suggestions for fully sequential design procedures. Alternative suggestions are made along with conjectures as to how these might improve performance. Chapter 6 presents a simulation study, the aim of which is to investigate the conjectures of Chapter 5. The results of this study provide empirical support for these conjectures. In Chapter 7 examples are analysed. These suggest aids to sequential experimentation by means of reduction of the dimension of the design space and the possibility of experimenting semi-sequentially. Further examples are considered which stress the importance of the use of prior information in situations of this type. Finally we consider the design of experiments when semi-sequential experimentation is mandatory because of the necessity of taking batches of observations at the same time. In Chapter 8 we look at some of the assumptions which have been made and indicate what may go wrong where these assumptions no longer hold.

Considering climate change in the development of marine protected areas

Marine ecosystems are facing a diverse range of threats, including climate change, prompting international efforts to safeguard marine biodiversity through the use of spatial management measures. Marine Protected Areas (MPAs) have been implemented as a conservation tool throughout the world, but their usefulness and effectiveness is strongly related to climate change. However, few MPA programmes have directly considered climate change in the design, management or monitoring of an MPA network. Under international obligations, EU, UK and national targets, Scotland has developed an MPA network that aims to protect marine biodiversity and contribute to the vision of a clean, healthy and productive marine environment. This is the first study to critically analyse the Scottish MPA process and highlight areas which may be improved upon in further iterations of the network in the context of climate change. Initially, a critical review of the Scottish MPA process considered how ecological principles for MPA network design were incorporated into the process, how stakeholder perceptions were considered and crucially what consideration was given to the influence of climate change on the eventual effectiveness of the network. The results indicated that to make a meaningful contribution to marine biodiversity protection for Europe the Scottish MPA network should: i) fully adopt best practice ecological principles ii) ensure effective protection and iii) explicitly consider climate change in the management, monitoring and future iterations of the network. However, this review also highlighted the difficulties of incorporating considerations of climate change into an already complex process. A series of international case studies from British Columbia, Canada; central California, USA; the Great Barrier Reef, Australia and the Hauraki Gulf, New Zealand, were then conducted to investigate perceptions of how climate change has been considered in the design, implementation, management and monitoring of MPAs. The key lessons from this study included: i) strictly protected marine reserves are considered essential for climate change resilience and will be necessary as scientific reference sites to understand climate change effects ii) adaptive management of MPA networks is important but hard to implement iii) strictly protected reserves managed as ecosystems are the best option for an uncertain future. This work provides new insights into the policy and practical challenges MPA managers face under climate change scenarios. Based on the Scottish and international studies, the need to facilitate clear communication between academics, policy makers and stakeholders was recognised in order to progress MPA policy delivery and to ensure decisions were jointly formed and acceptable. A Delphi technique was used to develop a series of recommendations for considering climate change in Scotland’s MPA process. The Delphi participant panel was selected for their knowledge of the Scottish MPA process and included stakeholders, policy makers and academics with expertise in MPA research. The results from the first round of the Delphi technique suggested that differing views of success would likely influence opinions regarding required management of MPAs, and in turn, the data requirements to support management action decisions. The second round of the Delphi technique explored this further and indicated that there was a fundamental dichotomy in panellists’ views of a successful MPA network depending upon whether they believed the MPAs should be strictly protected or allow for sustainable use. A third, focus group round of the Delphi Technique developed a feature-based management scenario matrix to aid in deciding upon management actions in light of changes occurring in the MPA network. This thesis highlights that if the Scottish MPA network is to fulfil objectives of conservation and restoration, the implications of climate change for the design, management and monitoring of the network must be considered. In particular, there needs to be a greater focus on: i) incorporating ecological principles that directly address climate change ii) effective protection that builds resilience of the marine and linked social environment iii) developing a focused, strong and adaptable monitoring framework iv) ensuring mechanisms for adaptive management.