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Bayesian Inference in Ecological and Epidemiological Models

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Bayesian Inference in Ecological and Epidemiological Models Bayesian Inference in Ecological and Epidemiological Models A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy Saritha Kalhari Kodikara B.Sc Special Degree (Statistics), University of Sri Jayewardenepura. School of Science College of Science, Health and Engineering RMIT University June 2020 Declaration I certify that except where due acknowledgement has been made, the work is that of the author alone; the work has not been submitted previously, in whole or in part, to qualify for any other academic award; the content of the thesis is the result of work which has been carried out since the official commencement date of the approved research program; any editorial work, paid or unpaid, carried out by a third party is acknowledged; and, ethics procedures and guidelines have been followed. I acknowledge the support I have received for my research through the provision of an Australian Government Research Training Program Scholarship. Saritha Kalhari Kodikara 24 June 2020 i \If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts he shall end in certainties.." Sir Francis Bacon Acknowledgements Undertaking this PhD has been a truly life-changing experience for me and it would not have been possible without the help I got from many great individuals. First and foremost, I wish to express my profound gratitude to my supervisors: Prof. Lewi Stone, Dr. Haydar Demirhan and Dr. Yan Wang for the continuous support given to me throughout my PhD study. I could not imagine having better supervisors for my PhD study. In particular, I am indebted to Prof. Lewi Stone for his insightful com- ments and encouragements, but also for the hard questions which inspired me to widen my research from many different perspectives. I am also thankful for the constructive feedback given on my writing which helped me to become a much better writer. Besides my supervisors, I would like to thank Dr. Simon Firestone for taking me on- board to work on a rather fascinating research problem and for the assistance given throughout its duration. I am extremely thankful to my dear friend Ayomi Marshall for her helpful comments and proofreading this thesis. I would also like to take this opportunity to be thankful to all teachers, friends, colleagues whom I have crossed paths with in this lifetime and for the experiences we shared, as they have shaped me into who I am today. I would also like to extend my gratitude to my family: my parents, and to my brother and sister, for supporting me spiritually throughout my PhD candidature and my life in general. Finally, I am thankful to Pubudu, who has been by my side and encouraging me through- out. This research outcome would have been impossible without your sincere love and patience. iii Contributions by others to the thesis This is a thesis `with publications' and contains six papers that are either published or under review that illustrate the research undertaken. While Chapters3,4,6 and7 are published as journal papers, Chapters5 and8 are still under review. Below I discuss my contribution to each chapter along with the contributions from others who have co-authored the publications resulting from this thesis. • Chapter3 has been published with the following information: Kodikara, S., Demirhan, H., and Stone, L. (2018). Inferring about the extinction of a species using certain and uncertain sightings. Journal of Theoretical Biology, 442:98{109 Author contributions: Saritha Kodikara - Developed underlying theory, analysed the data, and drafted the manuscript. Haydar Demirhan - Guided the research and edited the manuscript. Lewi Stone - Guided the research and edited the manuscript. • Chapter4has been published with the following information: Kodikara, S., Demirhan, H., Wang, Y., Solow, A., and Stone, L. (2020). Inferring extinction year using a bayesian approach. Methods in Ecology and Evolution, 11(8):964{973 Author contributions: Saritha Kodikara - Developed underlying theory, implemented and coded the model in R, analysed the data and drafted the manuscript. Haydar Demirhan - Guided the research and edited the manuscript. Andrew Solow - Guided the research and edited the manuscript. Yan wang - Guided the research and edited the manuscript. Lewi Stone - Guided the research and edited the manuscript. • Chapter5 is currently being prepared for publication: Author contributions: Saritha Kodikara - Developed underlying theory, implemented and coded the model in R, analysed the data and drafted the manuscript. Yan wang - Guided the research and edited the manuscript. Haydar Demirhan - Guided the research and edited the manuscript. Lewi Stone - Guided the research and edited the manuscript. • Chapter6 has been published with the following information: Thompson, C. J., Kodikara, S., Burgman, M. A., Demirhan, H., and Stone, L. (2019). Bayesian updating to estimate extinction from sequential observation data. Biological Conservation, 229:26{29 Author contributions: Colin J. Thompson - Developed underlying theory and drafted the manuscript. Saritha Kodikara - Co-developed underlying theory, analysed the data, edited the manuscript. Mark A. Burgman - Guided the research and edited the manuscript. Haydar Demirhan - Guided the research and edited the manuscript. Lewi Stone - Guided the research and edited the manuscript. • Chapter7 has been published with the following information: Thompson, C. J., Kodikara, S., Burgman, M. A., Demirhan, H., and Stone, L. (2020). Using survival theory models to quantify extinctions. Biological Conser- vation, 241:108345 Author contributions: Colin J. Thompson - Developed underlying theory and drafted the manuscript. Saritha Kodikara - Co-developed underlying theory, analysed the data, edited the manuscript. Mark A. Burgman - Guided the research and edited the manuscript. Haydar Demirhan - Guided the research and edited the manuscript. Lewi Stone - Guided the research and edited the manuscript. • Chapter8 is currently being prepared for publication.: Author contributions: Saritha Kodikara - Developed underlying theory, coded the model in C++, designed and conducted the simulations, and drafted the manuscript. Max S. Y. Lau - Guided the research and edited the manuscript. Mary van Andel - Guided the research and edited the manuscript. Mark A. Stevenson - Guided the research and edited the manuscript. Bryan T. Grenfell - Guided the research and edited the manuscript. Nigel French - Guided the research and edited the manuscript. Haydar Demirhan - Guided the research and edited the manuscript. Lewi Stone - Guided the research and edited the manuscript. Simon M. Firestone - Co-developed underlying theory, provided assistance with C++ coding, analysed the NZ data and edited the manuscript. To Amma, Thaththa, Aiya, Akka and to my soulmate/ best friend/ partner in crime Pubudu Perera. vi Contents Declarationi Acknowledgements iii Contributions by others to the thesis iv Contents vii List of Figuresx List of Tables xiii Abstract 1 1 Introduction3 1.1 Overview....................................3 1.2 Species extinction models...........................3 1.2.1 Significance...............................3 1.2.2 Objective................................5 1.2.3 Background...............................5 1.3 Infectious disease models............................ 10 1.3.1 Significance............................... 10 1.3.2 Objective................................ 13 1.3.3 Background............................... 13 1.4 Research questions addressed in the thesis.................. 16 1.5 Thesis Layout.................................. 17 2 Bayesian Approach 21 2.1 Markov chain Monte Carlo method...................... 26 2.1.1 Markov chain.............................. 26 2.1.2 Metropolis-Hastings algorithm.................... 28 2.1.3 Gibbs sampler............................. 28 2.2 Popularity of Bayesian approaches in ecology and epidemiology...... 29 3 Incorporating uncertainty in the sighting data into species extinction models 31 3.1 Introduction................................... 32 3.2 Data....................................... 33 3.3 Methods- Model 1............................... 34 vii Contents viii 3.4 Results- Model 1................................ 37 3.5 Methods- Model 2............................... 47 3.6 Results- Model 2................................ 49 3.7 Guideline to select between Models...................... 53 3.8 Discussion.................................... 55 4 Inferring Extinction Year using a Bayesian Approach 57 4.1 Introduction................................... 58 4.2 Model development............................... 60 4.2.1 Model 1 - Certain sightings only................... 61 4.2.2 Model 2 - Certain and uncertain sightings.............. 63 4.3 Results...................................... 65 4.3.1 Simulation Study............................ 65 4.3.2 Case study............................... 69 4.4 Sensitivity analysis............................... 75 4.4.1 Artificial sighting records....................... 76 4.4.2 Species sighting records........................ 77 4.5 Discussion.................................... 78 5 Modeling extinction of a species using non-homogeneous Poisson pro- cesses with a change-point 81 5.1 Introduction................................... 82 5.2 Model Development.............................. 83 5.3 Results...................................... 89 5.3.1 Black-footed ferret........................... 89 5.3.2 Ivory-billed woodpecker.......................
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