master thesis.pdf - Atrium - University of Guelph

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AcknowledgementsFirst and foremost, I would like to extend my gratitude to my advisor Dr.PaulMcNicholas for his constant guidance and support. His knowledge and enthusiasmin his respective fields have driven my motivation to conduct the research I presenthere. In addition, without his generous scholarship, my study in Canada would beinfeasible. I am very excited to continue my research with him.I would like to thank my advisory committee member Dr.Ryan Browne for hisvaluable suggestions during my Master study and thesis writing, and Drs. EdwardCarter, Rob Deardon for taking the time to be members of my Examining Committee.I hope the level of enjoyment they had while reading my thesis equated to thelevel of enjoyment I had while preparing it.To my family and friends, my sincere thanks for your endless encouragement throughoutmy life. I am where I am now because of your love and support. I am blessed tohave you all in my life. I love you with all my heart.iv
Table of ContentsList of TablesviiList of Figuresx1 Introduction 12 Background 42.1 Model-based clustering . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Model selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Merging mixture components . . . . . . . . . . . . . . . . . . . . . . 112.4 Comparing clusterings . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Methodology 163.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Top model selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4 Merging mixture components . . . . . . . . . . . . . . . . . . . . . . 203.5 Top model averaging . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Data Analyses 244.1 Real data examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24v
Page 2 and 3: ABSTRACTMixture Model Averaging for
Page 6 and 7: 4.1.1 Wine data . . . . . . . . . .
Page 8 and 9: 4.3 Results from top M model select
Page 10 and 11: List of Figures2.1 Contours of the
Page 12 and 13: and the information conveyed by the
Page 14 and 15: Chapter 2Background2.1 Model-based
Page 16 and 17: [ 0µ = , Σ =0][ ] 1 00 1µ =[ 00]
Page 18 and 19: the form:AIC = 2l(x, ˆϑ) − 2k,
Page 20 and 21: and cross-validation likelihood (Sm
Page 22 and 23: graphical diagnostics and proposed
Page 24 and 25: a) objects in the pair are placed i
Page 26 and 27: Chapter 3Methodology3.1 OverviewAs
Page 28 and 29: Table 3.1: Models available in the
Page 30 and 31: Case II1. Select the top 5 models (
Page 32 and 33: model after merging are calculated
Page 34 and 35: Chapter 4Data Analyses4.1 Real data
Page 36 and 37: Table 4.2: Results for top 5 model
Page 38 and 39: 4.1.2 Olive dataThe olive data, whi
Page 44 and 45: Figure 4.4: Pairs plot of the three
Page 46 and 47: subsequent models and the best mode
Page 48 and 49: The choice of weight is flexible. T
Page 50 and 51: Biernacki, C., G. Celeux, and G. Go
Page 52 and 53: Krivitsky, P. N., M. S. Handcock, A
Page 54:
ust covariance estimation via neare
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